Which rule do I apply first?

Work from the outside in: identify the overall structure (sum, product, quotient, composition) before differentiating the parts.

Derivative Rules — Examples and Uses

The differentiation rules you reach for in every calculus problem.

$\frac{d}{dx} x^n = n x^{n-1}$

Works for every real exponent n.

$(uv)' = u'v + uv'$

For a product of two functions of x.

$\left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2}$

Watch the order of terms in the numerator.

$\frac{d}{dx} f(g(x)) = f'(g(x)) g'(x)$

Differentiate the outer function, then multiply by the inner derivative.

Solve · Check · Learn

Enter a problem that uses one of these formulas and follow the worked steps.

Try:

Which rule do I apply first?: Work from the outside in: identify the overall structure (sum, product, quotient, composition) before differentiating the parts.