
find the derivative of the following functions wrt x
question = y = (sinx )^x
y= (sinx)^x Taking log, lny = x ln(sinx) Taking derivative wrt x, 1/y dy/dx = x (1/sinx)cosx + ln(sinx) Put y and simplyfy. Thanks and regards, Robin askIITian Faculty.
yesterday

1the normal to a curve at p (x,y) meets the xaxis at G if the dist of G from origin is...
P(x, y) and G(2x, 0) are 2 points on the normal. So, slope of the normal is, m=0y2xx=yx This means that the slope of the curve to which the normal was drawn is = 1m=xy Thus, the equation of the...
yesterday

how to solve functional equations
There are some common methods of solving them. For example, in dynamic programming a variety of successive approximation methods are used to solve Bellman`s functional equation, including methods...
yesterday

One side of an equilateral triangle is 24 cm. The mid points of its sides are joined to...
the first triangle we form length of the side become half &it continues so long as we calculate 24(3)+12(3)+6(3)+3(3)+3/2(3)+3/4(3)+..........=144
4 days ago

Why we calculate the nature of denominator before find out asymptotes? like to fimd out...
x=1 is the assymptote of the given eq we first check denominator because asymptotes are tangents at infinity so when the denominator tends to zero at that pt tangents are called asymptotes
4 days ago

Consider the infinite sequence {n1/n } i.e. 1 , 21/2 , 31/3 . . . . .Find the largest term...
nth term of the sequence is given by : (10n + 1)/n for n>1 Differentiate it : 0  1/n^2 It is always less than 0. Hence, it is decreasing always. Hence, the largest term is 21/2. Thanks Bharat...
6 days ago

Find the interval in which the function f(x) = x1/x is increasing?
f(x) = x  1/x f`(x) = 1 + 1/x^2 for increasing the f`(x) > 0 Here, f`(x) > 0 for all values of x. Hence, it is increasing in its entire domain. Thanks Bharat Bajaj IIT Delhi askiitians faculty
6 days ago

If x=(3at)/(a+t^3) and y=(3at^2)/(a+t^3) find dy/dx
First find dy/dt, dy/dt = (a+t^3). 6at  3at^2 ( 3t^2) / (a+t^3)^2 dx/dt = (a+t^3)(3a)  3at(3t^2)/(a+t^3)^2 Now divide both: dy/dx = (6a^2t 3at^4)/ (3a^2 3at^3) Thanks Bharat Bajaj IIT Delhi...
8 days ago

if y=ln((X^2+1)/(v14x^3)),x is not equal to 1
then find d^2y/dx^2 at x not equal to 1
AT X=1 SECOND DERIVAATIVE EXISTS
8 days ago

What are complex numbers? I mean what is their significance?
Imaginary/complex numbers are multiples of i. Like 2i, 4i, 2.881i etc... They arise because not all equations can be solved by using only real numbers. Real numbers are all numbers ranging from ...
12 days ago

Consider the infinite sequence {n1/n } i.e. 1 , 21/2 , 31/3 . . . . .Find the largest term...
21/210.5
31/310.3
41/410.25
this series dicreasing so 21/2 is greater
15 days ago

There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional...
The output for x no. of trees is then : (800  10n)(50+n) Hence, O = 300n  10n^2 + 40000 Differentiate it : 300  20n = 0 hence, n = 15 Hence, 15 trees should be added. Thanks Bharat Bajaj askiitians...
15 days ago

f(x)=x²x+1÷x²+x+1 find minimum value of f(x)
f(x) = x²x+1/ x²+x+1 = ( x²+x+1 2x )/ x²+x+1 Hence, f(x) = 1  2x/ x²+x+1 df(x)/dx = 0 x = 1, 1 Now find the value of d/dx(df(x)/dx) at x = 1,1 For x = +1, it is positive. Hence there is a minima...
15 days ago

Show that if f is in?nitely di?erentiable on (1, 1) and f(1/n)= 0 for all n > 1 then...
Be the first one to answer
16 days ago

Consider the infinite sequence {n1/n } i.e. 1 , 21/2 , 31/3 . . . . .Find the largest term...
nth term of the sequence is given by : (10n + 1)/n for n>1 Differentiate it : 0  1/n^2 It is always less than 0. Hence, it is decreasing always. Hence, the largest term is 21/2. Thanks Bharat...
16 days ago

LIM X>INFINITY X(SQUARE)+1/X+1  AX2B=3/2
lim x^2+1/(x+1)  ax2b=3/2 lim(x^2+1/x+1=x) lim xax2b=3/2 lim x(1a)2b=3/2 , give a=1 and b=3/4 sher mohammad b.tech, iit delhi
17 days ago

lim(n?8)??(lim(x?8)??(1^2 ?sin?^2 ø+2^2 ?sin?^2 ø…………)^ ? )^ ?/n^3 =
Dear Student , Please clear your question and post again. Please specify sign. Thanks & Regards Rinkoo Gupta AskIITians Faculty
19 days ago

please give the solution. Prove That
Dear student, Please clear your question and post again. Thanks & Regards Rinkoo Gupta AskIITians Faculty
19 days ago

derivative of x^x^x
y=x^x^x taking log on both sides, we get logy=xlog(x^x) =>logy=x.xlogx=x^2logx differentiating w. r. to x (1/y).dy/dx=x^2.(1/x)+logx.2x =x+2xlogx =x(1+2logx) dy/dx=y.x(1+2logx) =(x^x^x).x(1+2logx)...
19 days ago

Find all the values of ‘a’ for which (a + 2)x3  3ax2 + 9ax  1 = 0 decreases...
f'(x)=3(a+2)x^26ax+9a<0, for all x a+2<0, a<2 f''(x)=6(a+2)x6a=0 , x=0 the maxima of f'(x) should also be less than zero f'(0)=9a<0 imply a<2 sher mohammad b.tech, iit delhi
19 days ago

A rectangle is inscribed in an isosceles triangle with base 1 unit and height h units....
There is some correction in question. The rectangle cant have any minimum area. We will find out the maximum area. Let the triangle be ABC with BC on the x axis and point A on y axis. A(0,h) B(1/2,0)...
20 days ago

Define a function h : [0, 1] ? [1, 1] as h(x) = sin p[(2x^21)/2]. Using Inverse function...
As x belongs to [0,1], (2x^2  1)/2 goes from [1,1]. Take f(x) = f(y) for some x,y in domain, sin pi(2x^21/2) = sin p(2y^21/2) It implies that 2x^2  1 / 2 = 2y^2  1 / 2 THerefore, x = y Also, for...
20 days ago

Consider a function g(x) which is defined and differentiable on (8, 8) and increasing in...
f(x) = g(x)  (g(x))^2 + (g(x))^3 f'(x) = g'(x) ( 1  2 g(x) + 3g(x)^2) Now, 3g(x)^2  2g(x) + 1 has Discriminant = 0. Hence, this means that this is either always positive or always negative. g'(x)...
20 days ago

Consider the infinite sequence {n^1/n } i.e. 1, 2^1/2 , 3^1/3 . . . . .Find the largest...
f(n)= n^(1/n) log(f(n))= log(n)/n taking derivative both sides f'(n)/f(n)= (1/(n^2)log(n)/(n^2) f'(n)=(1log(n))f(n)/n^2 f'(n)=0 log(n)=1, n=e , which imply nearest integer is 3, for n=3 , the...
20 days ago

There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional...
let number of additional tree is n , now total trees =50+n apple production per tree =80010n total production =(50+n)(80010n) = (10n^2300n40000) f'(n)= 20n300=0 n=15 sher mohammad b.tech, iit...
20 days ago