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: $f'(x) = \frac{2}{x} + 4\cos x$.

$e^x$ is a unique function where its rate of change is always proportional to its current value.

It indicates that as $x$ increases, $\cos x$ decreases in the first quadrant, hence the negative rate of change.

They are fundamental building blocks used in conjunction with other rules like the product, quotient, and chain rules.

$f'(x) = \cos x$

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

$f'(x) = e^x$

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

4\cos x

$-2\sin x$

$\frac{5}{x}$