Click to Chat

1800-2000-838

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

• Statistics and Probability
• OFFERED PRICE: R 600
• View Details
Get extra R 600 off
USE CODE: chait6

				   what is dy/dx? how to understand it correctly and easily?


7 years ago

Share

										Hi,
In calculus, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point; for example, the derivative of the position (or distance) of a vehicle with respect to time is the instantaneous velocity (respectively, instantaneous speed) at which the vehicle is traveling. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. The process of finding a derivative is called differentiation. The fundamental theorem of calculus states that differentiation is the reverse process to integration.
Differentiation is a method to compute the rate at which a dependent output y changes with respect to the change in the independent input x. This rate of change is called the derivative of y with respect to x. In more precise language, the dependence of y upon x means that y is a function of x. If x and y are real numbers, and if the graph of y is plotted against x, the derivative measures the slope of this graph at each point. This functional relationship is often denoted y = ƒ(x), where ƒ denotes the function.
The simplest case is when y is a linear of x, meaning that the graph of y against x is a straight line. In this case, y = ƒ(x) = m x + c, for real numbers m and c, and the slope m is given by
$m={\mbox{change in } y \over \mbox{change in } x} = {\Delta y \over{\Delta x}}$
where the symbol Δ (the uppercase form of the Greek letter Delta) is an abbreviation for "change in." This formula is true because
y + Δy = ƒ(x+ Δx) = m (x + Δx) + c = m x + c + m Δx = y + mΔx.
It follows that Δy = m Δx.
This gives an exact value for the slope of a straight line. If the function ƒ is not linear (i.e. its graph is not a straight line), however, then the change in y divided by the change in x varies: differentiation is a method to find an exact value for this rate of change at any given value of x.
Rate of change as a limiting value

The tangent line at (x, ƒ(x))

such an infinitesimal change in x is denoted by dx, and the derivative of y with respect to x is written $\frac{dy}{dx} \,\!$
suggesting the ratio of two infinitesimal quantities.

The secant to curve y= ƒ(x) determined by points (x, ƒ(x)) and (x+h, ƒ(x+h))

The tangent line as limit of secants

the difference between the x values, that is, $m = \frac{\Delta f(x)}{\Delta x} = \frac{f(a+h)-f(a)}{h}.$
The derivative is the value of the difference quotient as the secant lines approach the tangent line. Formally, the derivative of the function ƒ at a is the limit
$f'(a)=\lim_{h\to 0}{f(a+h)-f(a)\over h}$
of the difference quotient as h approaches zero, if this limit exists. If the limit exists, then ƒ is differentiable at a. Here f′ (a) is one of several common notations for the derivative

Regards,
Rajat


7 years ago

# Other Related Questions on Vectors

what is a scalar?

HAI GURAVAIAH, THE SCALAR IS DEFINED BY THE PRODUCT OF THE TWO SCALAR PRODUCTS IS CALLED THE SCALAR. THANK TOU..................

 Gowri sankar one year ago

In physics, a scalar is a one-dimensional physical quantity, i.e. one that can be described by a single real number (sometimes signed, often with units), in other words a scalar is a...

 raj one year ago

Dear Guravaiah In physics, a scalar is a one-dimensional physical quantity, i.e. one that can be described by a single real number (sometimes signed, often with units), in other words a...

 Prabhakar ch one year ago
What is the parallelogram law of two vectors and what is definations of dot product and cross product

Acccording to the parallelogram law of vector addition: "If two vector quantities are represented by two adjacent sides or a parallelogram. then the diagonal of parallelogram will be equal...

 KALYAN one year ago

HELLO PRABHAKAR parallelogram law of vector addition states that when two vectors are represented by two adjacent sides of a parallelogram by direction and magnitude then the resulatant of...

 raj one year ago

in parallelogram of vectors two vectors are represented by two adjacent sides in parallelogram of vectors the square of the diagonal is equal to squre root of two adjacent sides squares and...

 RAMCHANDRARAO one year ago

a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another. a matrix with one row or one column. Computing denoting a...

 Prabhakar ch one year ago

a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another. a matrix with one row or one column. Computing denoting a...

 raj one year ago

hi ,,,,,,,,chetan.. a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another. a matrix with one row or one column....

 T.kumar one year ago
If alpha is a real root of the equation ax 2 +bx+c and beta is a real root of equation -ax 2 +bx+c. Show that there exists a root gama of the equation (a/2)x 2 +bx+c which lies between alpha...

 Ajay 6 months ago

Small Mistake in last para posting again..............................................................................................................

 Ajay 6 months ago

We have Similarly, So if P(x) = a/2 x 2 +bx +c, then and are off opposite sign and hence there must exist a root between the two numbers.

 mycroft holmes 6 months ago
In the listed image can you tell me how beta*gamma = 2 ….. . . .. ??

The value of gamma is still not correct, either printing mistake or you gave me wrong value. The correct value of gamma is below

 Ajay 5 months ago

Thankyou so much............................. …......................................................................!

 Anshuman Mohanty 5 months ago

Yes sorry..... . . . .it is not so clear.. ok the values are beta = α + α^2 + α^4 and gamma = α^3 + α^5 + α^7

 Anshuman Mohanty 5 months ago
if |z - i| Options: a*) 14 b) 2 c) 28 d) None of the above

If |z-i| = ?? PLs complete the question

 Nishant Vora one month ago

Got it! [z + 12 – 6 i ] can be rewritten as [ z – i + 12 – 5 i] => | z – i | and => |12 – 5 i | = sqrt ( 12^2 + 5^2) = 13......................(2) => | z + 12 – 6 i | => | z + 12 – 6 i |...

 Divya one month ago

I tried posting the question several times, it kept cutting off the rest of the question. Here: If | z-1| Options: a*) 14 b) 2 c) 28 d) None of the above

 Divya one month ago
View all Questions »

• Complete JEE Main/Advanced Course and Test Series
• OFFERED PRICE: R 15,000
• View Details
Get extra R 6,000 off
USE CODE: chait6

• Statistics and Probability
• OFFERED PRICE: R 600
• View Details

Get extra R 600 off
USE CODE: chait6

More Questions On Vectors