# How to differentiate these functions?

+1 vote

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

2. 6/√(3x - 5)

asked Feb 13, 2013 in CALCULUS

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

selected Feb 14, 2013 by potatoes

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

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

• 1). f(x) = 1/(4x - 2)3 .

f(x) = (4x - 2)- 3

Power rule for derivatives : if f(x) = xn, then f '(x) = nxn - 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) = nxn - 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 .