# How do you find the derivative of this equation e^(3x - 4 cos x)?

Oct 24, 2016

$\left(3 + 4 \setminus \sin x\right) {e}^{3 x - 4 \setminus \cos x}$

#### Explanation:

Before we tackle this problem, let's review the derivative of an exponential function.

The definition for an exponential function is defined as follows:

$\setminus \frac{d}{\mathrm{dx}} {e}^{f \left(x\right)} = f ' \left(x\right) \setminus \cdot {e}^{f \left(x\right)}$

In this case, we have:
$f \left(x\right) = 3 x - 4 \setminus \cos x$

The derivative of $3 x$ is simply $3$ (power rule), and the derivative of the trigonometric function $\setminus \cos x$ is $- \setminus \sin x$. Hence,

$f ' \left(x\right) = 3 - \left(- 4 \setminus \sin x\right) = 3 + 4 \setminus \sin x$

Plugging it back into our formula for the exponential function, we obtain:

$\left(3 + 4 \setminus \sin x\right) {e}^{3 x - 4 \setminus \cos x}$

• htriber