AP EAMCET2002MathematicsDifferentiation
Let f(x)=e^x, g(x)= ⁻¹ x and h(x)=f(g(x)) , then h^ (x) h(x) is equal to
Options
- A⁻¹ x
- B1 1-x^2
- C- 1 1-x^2
- De^ ⁻¹ x
Correct answer
B. 1 1-x^2
Step-by-step solution
We have, aligned h(x) & =f(g(x))=f ( ⁻¹ x ) h(x) & =e^ ⁻¹ x h(x) & = ⁻¹ x aligned On differentiating w.r.t. x , we get h^ (x) h(x) = 1 1-x^2