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What actually IS 'differentiation'?

Differentiation is a really common technique in a branch of maths called calculus. The idea is that you have a line on a graph (or a 'function') and we want to know the gradient - the steepness - of that cur...
BT
Answered by Ben T. • Maths tutor
3850 Views

Sketch the graph of f(x) = sin(x). On the same set of axes, draw the graph of f(x)+2, f(2x) and f(-x). By observing your graphs of f(x) and f(x), if f(a)=1, what is the value of f(-a)?

The first stage is the simple drawing of the sin graph. (could be done on the whiteboard)Then it is a typical A-Level style question to perform three types of transformations on that graph, here we have 1. t...
JG
Answered by Jessica G. • Maths tutor
4824 Views

Differentiate the function y = 26 + x - 4x³ -½x^(-4)

dy/dx = 1 - 12x² + 2x^(-5)
LM
Answered by Louix M. • Maths tutor
3573 Views

Consider an isosceles triangle ABC, where AB=AC=1, M is the midpoint of BC, and <BAM=<CAM=x. Use trigonometry to find an expression for BM and by finding BC^2, show that cos2x = 1 - 2(sinx)^2.

Consider the right-angled triangle BAM. We have the hypotenuse and an angle, and want to find the opposite side. Therefore, using SOHCAHTOA, sinx = BM/1, hence BM = sinx. Because M is the midpoint of BC, BC ...
BS
Answered by Blessie S. • Maths tutor
6890 Views

Solve 5x + 10 = 2x(5x + 10)

First multiply out the right hand side to get5x + 10 = 10x^2 + 20xThen rearrange so everything equals zero, forming a quadratic equation10x^2 + 15x - 10 = 0 To make things easier, you can simplify the equati...
AM
Answered by Amy M. • Maths tutor
4476 Views