Question

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

Answer 1

`(3 + 4\sin x)e^{3x - 4\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:

`\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}`

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