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

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

Grade:11

2 Answers

Arun
25758 Points
4 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)
Shiva Prasad
13 Points
4 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)!

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