Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
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

  1. A⁻¹ x
  2. B1 1-x^2
  3. C- 1 1-x^2
  4. 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

Practice Differentiation on Quantrex Academy →

More from Differentiation

The domain of the derivative of the function f(x)= x 1+|x| is 2025If x= 2^ cosec ⁻¹ t and y= 2^ ⁻¹ t ,|t| 1 then d y d x = 2025If (a+ 2 b x)(a- 2 b y)=a^2-b^2 where a>b>0 , then at ( 4 , 4 ) , dy dx = 2025If x y - y x =0 , then d y d x = 2025If y = ( _ x x )^ x , then dy dx = 2025If f(x)=x^ Sec ⁻¹ x , then f^ (2)= 2025If y= x^4 3 x-5 (x^2-3 )(2 x-3) , then ( d y d x )_ x=2 = 2025If x^2+y^2+ y=4 , then the value of d^2 y d x^2 at x=-2 is 2025 Full Differentiation list All AP EAMCET PYQs