find the derivative of 5x divided by (x+4)^2?

Question

please provide a step by step process and solution

Answer 1

I love these questions..... it's easy
DO YOUR OWN HOMEWORK

Answer 2

f(x) = 5x / (x + 4)^2

To find the derivative, we use the quotient rule, which goes as follows, verbally: "The derivative of the top times the bottom, minus the derivative of the bottom times the top, over the bottom squared."

f'(x) = [5(x + 4)^2 - 2(x + 4)(5x)] / [ (x + 4)^2 ]^2

Note that squaring a square makes it to the power of 4.

f'(x) = [5(x + 4)^2 - 2(x + 4)(5x)] / (x + 4)^4

Simplify the numerator,

f'(x) = [5(x^2 + 8x + 16) + 10x(x + 4)] / (x + 4)^4
f'(x) = [5x^2 + 40x + 80 + 10x^2 + 40x] / (x + 4)^4
f'(x) = [15x^2 + 80x + 80] / (x + 4)^4

Factoring out a 5, we get

f'(x) = 5(3x^2 + 16x + 16) / (x + 4)^4

Factoring the numerator,

f'(x) = 5(x + 4)(3x + 4) / (x + 4)^4

Notice that we can cancel the (x + 4) using the denominator of
(x + 4)^2. This will reduce the power of the denominator.

f'(x) = 5(3x + 4) / (x + 4)^3

This is actually as simple as it gets.

Answer 3

it is 5/2(x+4)