How to differentiate these functions?

Question

1. 1/(4x - 2)^3

2. 6/√(3x - 5)

Answer 1

1) f(x)=1/(4x - 2)^3

Using the Quotient Rule of differention,

d/dx(u/v)=(vu'-uv')/v^2

f'(x)=((4x - 2)^3)*(d/dx(1))-(1*(d/dx(4x - 2)^3)/((4x - 2)^3)^2

         =0-(3(4x - 2)^2*(4))/((4x - 2)^6)

         =-12((4x - 2)^2/((4x - 2)^6

         =-12/(4x - 2)^4

Differention of function is -12/(4x - 2)^4

Answer 2

2) f(x)=6/√(3x - 5)

Using the Quotient Rule of differention, d/dx(u/v)=(vu'-uv')/v^2

f'(x)=((√(3x - 5))*(d/dx(6))-(1*(d/dx(√(3x - 5))/((√(3x - 5))^2

      =0-((1/2)(3x - 5)^(-1/2)*(3))/3x - 5

     =-(3/2)((3x - 5)^(-1/2))/3x - 5

       =-(3/2)(3x - 5)^(-3/2)

Differentiation of function is -(3/2)(3x - 5)^(-3/2)

I hope that helps u

Comments

Differentiation of 6/√(3x - 5) is - 9/(3x - 5)^3/2 .

Answer 3

• 1). f(x) = 1/(4x - 2)³ .

f(x) = (4x - 2)^{- 3}

Power rule for derivatives : if f(x) = xⁿ, then f '(x) = nx^{n - 1}.

f '(x) = - 3(4x - 2)^{- 3 - 1} (4x - 2) '

= - 3(4x - 2)^{- 4} (4)

= - 12/(4x - 2)⁴ .

 ∴ Differentiation of 1/(4x - 2)³ is -12/(4x - 2)⁴ .

• 2). f(x) = 6/√(3x - 5).

f(x) = 6(3x - 5)^-1/2

Power rule for derivatives : if f(x) = xⁿ, then f '(x) = nx^{n - 1}.

f '(x) = 6[(-1/2)(3x - 5)^{-1/2 - 1}]*(3x - 5) '

= - 3 * (3x - 5)^-3/2 * 3

= - 9/(3x - 5)^3/2 .

 ∴ Differentiation of 6/√(3x - 5) is - 9/(3x - 5)^3/2 .