Question

How do you differentiate `f(x)=(4x)/(2x+3)^2` using the quotient rule?

Answer 1

Answer: `h'(x)=1/4(9-8x^2)/(x+2)^4`

Explanation:

Quotient rule of differentiating states that, given a function
`h(x)= f(x)/g(x)` then
a) `h'(x)=[f'(x)g(x)-f(x)g'(x)]/[g(x)]^2`
Let `f(x)=4x and g(x)= (2x+3)^2`
b) Differentiate `f(x)=>f'(x) and g(x)=>g'(x)`
`f'(x) = 4; g'(x)= 4(2x+3)`
c) insert b) into a)
d) `h'(x)=[4*(2x+3)^2-4x*4(2x+3) ]/(2x+3)^4`
Answer: `h'(x)=1/4(9-8x^2)/(x+2)^4`