Question

How do you find f'(1) if f(x)=x2⋅tan−1x?

Answer 1

f(x) = x^2 * tan^-1 x

Differentiating this with respect to x on both sides,

f'(x) = x^2/1+x^2 + tan^-1 x * 2x

So,

for f'(1), we'll have to put in the value of 1 in place of x in the expression.

So,

f'(1) = (1)^2/1+(1)^2 + tan^-1 1 *2(1)

= 1/2 + π/4*2

= (1+π)/2

Therefore,

f'(1)= {1+π/2}

This is the final answer !