+91-87964 74404
FlagBACK
Question icon
Grade 11Differential Calculus

Find the derivative of y = (1-x)(2-x)....(n-x) at x=1

Profile image of Ajudiya Janvi
8 Years agoGrade 11
Answers icon

2 Answers

Profile image of Arun
8 Years ago
Dear student
 
In the derivative inly one term is left if x=1 is put
Then
f'(x) = -1(2-x)(3-x)(4-x)......(n-x)
At x = 1
= -1*2*3*4*5*6*....(n-1)
= - (n-1)!
 
Regards
Arun (askIITians forum expert)
Profile image of Shiva Prasad
8 Years ago
Derivative of y=(1-x)(2-x).......(n-x)
 
dy/dx(uvw)=u’vw+uv’w+uvw’
 
 
\frac{\mathrm{d}y }{\mathrm{d} x}= -1(2-x)(3-x).....(n-x) +(1-x)(-1)(3-x)....(n-x)+......+......+(1-x)(2-x)........(n-1-x)(-1) \;
 
at x=1,only one term will be left as other terms include (1-x) become zero.
 
{\color{Red} \frac{\mathrm{d}y }{\mathrm{d} x}_{_{at (x=1)}}}= -1(2-1)(3-1).....(n-1) +0+......+......+0
 
                   \Rightarrow -1.(1)(2).....(n-1)
                  \Rightarrow -1(n-1)!

Other Related Questions on differential calculus

question mark
the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution to  move once over to level a playground. find the area of the playground in square m?
differential calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
Find dy/DX when y=x^sinx+sin-1√x.
 
Please give me the solution of this problem. 
differential calculus
1 Answer Available

Last Activity: 4 Years ago

question mark
If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.
differential calculus
1 Answer Available

Last Activity: 4 Years ago

question mark
Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.
differential calculus
1 Answer Available

Last Activity: 4 Years ago

question mark
Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin C
where A + B + C = T
(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.
differential calculus
1 Answer Available

Last Activity: 4 Years ago