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

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Answer 1 · 2016-10-24T03:24:27

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

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

The definition for an exponential function is defined as follows:

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

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

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

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

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

$(3 + 4 \sinx)e^{3x - 4\cos x}$

How do you find the derivative of this equation e^(3x - 4 cos x)e3x−4cosxe^(3x - 4 cos x)?