Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202616 April 2026Morning ShiftMathematicsDifferentiationActual

The derivative of ₈( ₅ x) w. r. t. x is

Options

  1. A1 ₅ 8 x
  2. B1 x 5 x
  3. C1 x x 8 5
  4. D1 x 8 x

Correct answer

D. 1 x 8 x

Step-by-step solution

Let y = ₈( ₅ x) Using the change of base formula, we can write: y = _e( ₅ x) _e 8 Differentiating with respect to x using the chain rule: dy dx = 1 _e 8 1 ₅ x d dx ( ₅ x) dy dx = 1 _e 8 1 ₅ x 1 x _e 5 Substitute ₅ x = _e x _e 5 : dy dx = 1 _e 8 _e 5 _e x 1 x _e 5 dy dx = 1 x _e 8 _e x Assuming represents the natural logarithm _e , we get: dy dx = 1 x 8 x Answer: 1 x 8 x

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 MHT CET PYQs