# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(5\cdot e^{7x}\cdot \cos\left(9x\right)\right)$

Learn how to solve product rule of differentiation problems step by step online.

$5\frac{d}{dx}\left(e^{7x}\cos\left(9x\right)\right)$

Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule (d/dx)(5e^(7x)*cos(9*x)). The derivative of a function multiplied by a constant (5) is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=e^{7x} and g=\cos\left(9x\right). The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). The derivative of the linear function times a constant, is equal to the constant.

$5\left(7e^{7x}\cos\left(9x\right)-9e^{7x}\sin\left(9x\right)\right)$
$\frac{d}{dx}\left(5\cdot e^{7x}\cdot \cos\left(9x\right)\right)$

### Main topic:

Product rule of differentiation

### Time to solve it:

~ 0.05 s (SnapXam)