# How do you differentiate  f(x)= (4x^2+5)(3x-5) using the product rule?

Mar 15, 2018

#### Answer:

$8 x \left(3 x - 5\right) + 3 \left(4 {x}^{2} + 5\right)$
$36 {x}^{2} - 40 x + 15$

#### Explanation:

First the product rule is, $f \left(x\right) = g p r i m e \left(x\right) h \left(x\right) + h p r i m e \left(x\right) g \left(x\right)$

Where $g \left(x\right) = \left(4 {x}^{2} + 5\right)$
And $h \left(x\right) = \left(3 x - 5\right)$

Now take the derivative of both, this gives you...
$g p r i m e \left(x\right) = \left(8 x\right)$
$h p r i m e \left(x\right) = \left(3\right)$

So now plug into the product rule formula
$\left(8 x\right) \left(3 x - 5\right) + \left(3\right) \left(4 {x}^{2} + 5\right)$

After multiplying you get
$24 {x}^{2} - 40 x + 12 {x}^{2} + 15$

You then combine like terms and get the answer which is
$36 {x}^{2} - 40 x + 15$