M7 - Expert

Exponential and logarithm

y = a^x ; log_a(a^x) = x

A logarithm answers "what power gives this number".

Sine and cosine rules

a/sin A = b/sin B ; c^2 = a^2 + b^2 - 2ab cos C

Use the sine rule for pairs of side and angle, the cosine rule for three sides or two sides and the included angle.

Derivative of a power

d/dx (x^n) = n x^(n-1)

Bring the power down and reduce it by one.

Sum, product and quotient rules

(uv)' = u'v + uv' ; (u/v)' = (u'v - uv') / v^2

Differentiate sums term by term; use the product and quotient rules for combinations.

Tangent line and stationary points

y = f(a) + f'(a)(x - a)

The derivative at a point is the slope of the tangent. Stationary points have f'(x) = 0.

Integrals

integral of x^n = x^(n+1)/(n+1) + C

Integration undoes differentiation and measures the area under a curve.