dse question doubt

[bhavya jain]

someone plz tell me how to solve this question;
Q) Consider the function defined by f(x)=x^6+5x^4+2, for all x>=0. The derivative of its inverse function evaluated at f(x)=8, is
a)1/7
b)1/15
c)1/26
d)1/30

[econ14]

is it (c)?

[Arushi :))]

step1: find that value in f's domain where here the function attains value of 8
keeping f(x)=8
and solving for x we get x = 1.
step2: find the derivative of f at this point.. i.e 1
f'(1)=26
step3: the derivates of inverse functions are reciprocals of each other
so g'(8)= 1/f'(1)
hence the ans is 1/26

[bhavya jain]

Thanks a lot Arushi.