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.

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

Works for every real exponent n.

$(uv)^{'} = u^{'} v + u v^{'}$

For a product of two functions of x.

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

Watch the order of terms in the numerator.

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

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.