Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202422 May 2024Evening ShiftMathematicsDifferentiationActual

If f(x)=5 ^3 x-3 ^2 x and g(x)=4 ^3 x+ ^2 x , then the derivative of f(x) with respect to g(x) is

Options

  1. A5 x+2 6 x-1
  2. B- ( 5 x+2 6 x-1 )
  3. C15 x-6 12 x+2
  4. D- ( 15 x+6 12 x-2 )

Correct answer

D. - ( 15 x+6 12 x-2 )

Step-by-step solution

aligned & f(x)=5 ^3 x-3 ^2 x, g(x)=4 ^3 x+ ^2 x & d f(x) d x =-15 ^2 x x-6 x x & d g(x) d x =12 ^2 x x-2 x x & d f(x) d g(x) = -15 ^2 x x-6 x x 12 ^2 x x-2 x x = -15 x-6 12 x-2 aligned

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