Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2021MathematicsDifferentiationActual

What is the derivative of e^x with respect to x^e ?

Options

  1. Ax e^x e x^e
  2. Be^x x^e
  3. Cx e^x x^e
  4. De^x e x^e

Correct answer

A. x e^x e x^e

Step-by-step solution

Let y=e^x, d y d x =e^x aligned & and z=x^e d z d x =e x^ (e-1) & Now, d y d z = d y / d x d z / d x = e^x e x^ (e-1) = x e^x e x^e aligned

Practice Differentiation on Quantrex Academy →

More from Differentiation

Passage: Let (e^y )^x-y=0 , where y is a function of x whose domain is (0,10] . Question: What is dy dx equal to, given that y=y₀ when x=1 ? 2026If [4] y =x+ x^2+4 , then what is x^2+4 , dy dx equal to ? 2026Passage: Let (e^y )^x-y=0 , where y is a function of x whose domain is (0,10] . Question: What is dy dx equal to ? 2026For the following two (02) items: Consider the function f(x) = cases 4(5^x), & x What is f'(-1) equal to? 2025Consider the following for the two (02) items that follow: Let x = - and y = ^4 - ^4 . What is ( dy dx )^2 equal to? 2025Consider the following for the two (02) items that follow: Let (x+y)^ p+q = x^p y^q , where p , q are positive integers. The derivative of y with respect to x 2025Consider the following for the two (02) items that follow: Let y = ⁻¹ (x - 4x^3 27 ) . What is dy dx equal to? 2025For the following three (03) items: Let y = f(x) = x ⁻¹ x 1 - x^2 + 1 - x^2 . If x = , then what is dy dx equal to? 2025 Full Differentiation list All NDA PYQs