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Differentiation formulae

The 7 results the differentiation notes display, each with the conditions it needs to be true and a link to the lesson that states it. Of the 7, the formulae booklet prints 2, 4 are yours to memorise and 1 is a working line the notes derive in front of you.

Years 12-13 · 5 lessons with formulae.

A result the Edexcel formulae booklet prints is marked as such; one it does not print is marked to learn; and a result badged derived in the lesson is a working line the notes build in front of you rather than a standard result to memorise.

5 lessons

The derivative from first principles

f'(x) = \text{lim}_{h → 0} \frac{f(x + h) − f(x)}{h}

IN THE FORMULAE BOOKLETConditionsThe limit must exist, which is what it means for f to be differentiable at x.

Differentiating powers of x

y = x^{n} \, ⇒ \, \frac{dy}{dx} = nx^{n−1}

NOT IN THE BOOKLET: LEARN ITConditionsAny real n, with x ≠ 0 when n is negative and x > 0 where a non-integer power needs it.

Differentiating trig, exponentials and logs

\sin kx → k\cos kx, \, \cos kx → −k\sin kx

NOT IN THE BOOKLET: LEARN ITConditionsx in radians. Both derivatives are wrong in degrees.

e^{kx} → ke^{kx}, \, \text{ln } x → \frac{1}{x}

NOT IN THE BOOKLET: LEARN ITConditionsln x needs x > 0.

The product, quotient and chain rules

\frac{dy}{dx} = \frac{dy}{du} × \frac{du}{dx}

NOT IN THE BOOKLET: LEARN ITConditionsy differentiable in u and u differentiable in x.

(\frac{u}{v})' = \frac{u'v − uv'}{v^{2}}

IN THE FORMULAE BOOKLETConditionsu and v differentiable, and v ≠ 0.

Implicit and parametric differentiation

\frac{dy}{dx} = \frac{1}{dx/dy} = \frac{1}{\cos y}

NOT IN THE BOOKLET: DERIVED IN THE LESSONConditionsdx/dy must be non-zero and finite; here that means cos y ≠ 0.

Every formula in the library is indexed by unit on the equation index, and the differentiation notes are where these results are derived and used. The 4 the booklet does not print are on the list of every formula to memorise, alongside the rest of the course.

Also: Exponentials and logarithms formulae · Integration formulae