Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2023MathematicsDifferentiationActual

The derivative of e^ x^3 with respect to x is

Options

  1. Ae ^ x ^3
  2. B3 x ^2 2 e ^ x ^3
  3. C3 x ^3 e ^ x ^3
  4. D3 x ^3 e ^ x ^3 +3 x ^2

Correct answer

C. 3 x ^3 e ^ x ^3

Step-by-step solution

Let y= e ^ x ^3 , z = x On differentiating w.r.t.x, we get d y d x =e^ x^3 (3 x^2 )=3 x^2 e^ x^3 and d z d x = 1 x d y d z = d y d x d z d x = 3 x^2 e^ x^3 ( 1 x ) =3 x^3 e^ x^3

Practice Differentiation on Quantrex Academy →

More from Differentiation

If x 1+y +y 1+x =0 , then d y d x = 2024If y= ⁻¹ ( x -x 1+x^ 3 2 ) , then y^ (1) is equal to 2024At x= ^2 4 , d d x ( ⁻¹( x )+ ⁻¹ (e^x ) )= 2024The slope of the tangent to the curve x=3 t^2+1 , y=t^3-1 at x=1 is: 2023If y^x=e^ y-x , then d y d x is equal to 2023If f ( x )= 1+ ^2 ( x ^2 ) , then the value of f^ ( 2 ) 2023If y= ( 1+ 2 1- 2 ) , then d y d at = 3 4 is : 2023If 2^ x +2^ y =2^ x+y , then d y d x = 2021 Full Differentiation list All BITSAT PYQs