# How do you differentiate g(x) = (6x+9)cos(5x)  using the product rule?

Dec 16, 2016

$6 \left(\cos \left(5 x\right)\right) - \left(6 x + 9\right) \left(5 \sin \left(5 x\right)\right)$

#### Explanation:

Using the product rule is easier then you think. Just remember One simple rule.

${u}^{'} v + u {v}^{'}$
Where u and v are two different functions

Getting on the question. You have to take derivitave of the first function times it by the regular second function. You then have to add the normal first function and then times it by the derivative of the second function.

$U = \frac{d}{\mathrm{dy}} 6 x + 9 = 6$
$V = \frac{d}{\mathrm{dy}} \cos \left(5 x\right) = - 5 \sin \left(5 x\right)$

Plugging in the equation.

$\left(6\right) \left(\cos \left(5 x\right)\right) + \left(6 x + 9\right) \left(- 5 \sin \left(5 x\right)\right)$

Just a recap, The 6 is the derivative of the U. cos(5x) is the original function. You then add to 6x+9, which is the original function and then time the derivitive of the second function which is (-5sin(5x))
You can then simplify the function just a little by just bringing any negative signs to the front of an equation.
$6 \left(\cos \left(5 x\right)\right) - \left(6 x + 9\right) \left(5 \sin \left(5 x\right)\right)$