Top answers

Given that y = x^4 tan(2x), find dy/dx

Here we have a product of two functions - they are being multiplied together - so we need to use the product rule. The product rule is: if y = u·v, dy/dx = v·u' + u·v' (where f' stands for df/dx). u = x^4 du...
DB
Answered by Douglas B. • Maths tutor
11039 Views

Find the first four terms in the binomial expansion of (2 + x) ^5

Firstly we must take the 2 out of the bracket, as a binomial expansion must have a coefficent of 1 (2 + x) 5 = 2 5 (1 + 0.5x) 5 Then, it is a good idea to quote the binomial expasion formula (you can often p...
FO
Answered by Fiona O. • Maths tutor
20289 Views

Find and classify all the stationary points of the function f(x) = x^3 - 3x^2 + 8

Stationary points occur when the gradient of the function is zero. They can be visualised on a graph as hills (maximum points), as troughs (minimum points), or as points of inflection. (I would draw all thre...
RB
Answered by Ryan B. • Maths tutor
13922 Views

Differentiate y = (sin(x))^2 (find dy/dx)

This a relatively simple question which requires the use of the chain rule to solve. First we set u = sin(x) so we then have y = u 2 . Next we perform do differentiations, one on u as a function of x and the...
TC
Answered by Tabraiz C. • Maths tutor
19406 Views

Solve these simultaneous equations: 2x+y-5=0 and x^2-y^2=3

To solve this problem, you need to: rearrange the first equation (1) to express y in terms of x to obtain equation (3). Then, substitute this new equation into the quadratic one (the second equation from the...
NB
Answered by Nana B. • Maths tutor
5843 Views