$f'(x) = \cos x$

$f'(x) = -\sin x$

$f'(x) = e^x$

$f'(x) = \frac{1}{x}$

$4\cos x$

$-2\sin x$

$\frac{5}{x}$

1. Apply the constant multiple rule and derivative of $\sin x$. 2. Apply the power rule to $2x^2$. 3. Combine the results: $f'(x) = 3\cos x + 4x$.

1. Apply the constant multiple rule and derivative of $e^x$. 2. Apply the derivative of $\cos x$. 3. Combine the results: $f'(x) = 5e^x + \sin x$.

1. Apply the constant multiple rule and derivative of $\ln x$. 2. Apply the constant multiple rule and derivative of $\sin x$. 3. Combine the results: $f'(x) = \frac{2}{x} + 4\cos x$.

The instantaneous rate of change of a function with respect to its variable.

A trigonometric function that represents the ratio of the opposite side to the hypotenuse in a right triangle.

A trigonometric function that represents the ratio of the adjacent side to the hypotenuse in a right triangle.

The exponential function with base $e$, where $e$ is Euler's number (approximately 2.71828).

The natural logarithm function, which is the logarithm to the base $e$.