Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

Differentiate $f(x) = x^m(a x+b)^n$.

Differentiate $\displaystyle (ax^m+bx^2+c)^{n}$.

Rewriting fractional expressions involving $\sqrt[n]{x^m}$ using rules to combine and simplify indices. 

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Recovering original function given some information such as derivative and value at some point.

Introduction to using the product rule

Differentiate $\displaystyle \ln((ax+b)^{m})$

Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$

Differentiate $\displaystyle (ax^m+b)^{n}$.

Using indices rules to rewrite an expression from $\left(\frac{a^n}{b^n}\right)^{-1/n}$ to $\frac{b}{a}$.

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $\frac{1}{b}$, for integers $a$, $b$, $m$ and $n$.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

Use the product rule (number of ways of doing A and B = (no. for A)*(no. for B)) to count the number of ways of doing two independent tasks.

Simple application of "Power Rule" to differentiate single term functions.

All co-efficients and powers are integer (though some may be negative.

Fairly simple questions using differentiation "power rule" and "sum or difference rules" to differentiate single term functions and polynomials.

Some co-efficients and indices can be negative and/or fractional.

Calculating the missing side-length of a triangle using the cosine rule.

Given two angles and a side-length of a triangle, use the sine rule to calculate an unknown side-length.