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Factorise and solve: x^2 - 8x = -15

Step 1 : The first step is to rewrite the equation in the form a x 2 + b x + c = 0. So in this case, we achieve this by adding 15 to both sides: x 2 - 8x + 15 = -15 + 15 x 2 - 8x + 15 = 0 Step 2: Now we need...
MJ
Answered by Maisie J. • Maths tutor
7969 Views

Write tan(3x) in terms of tan(x). Hence show that the roots of t^3 - 3t^2 - 3t + 1 = 0 are tan(pi/12), tan(5pi/12) and tan(3pi/4)

The first part is relatively simple. If we write tan(3x) as tan(2x+x) we can use addition formulae to give: tan(2x+x)= (tan(2x)+tan(x))/(1-tan(2x)tan(x)) tan(2x) = 2tan(x)/(1-tan^2(x)) Substituing this in an...
DG
Answered by Daniel G. • Maths tutor
54015 Views

differentiate y = (4-x)^2

This is a basic example of a very important result: the chain rule. The difficulty of this sort of example is that we have a "function of a function". That is, we have the function '4-x' and then w...
BB
Answered by Ben B. • Maths tutor
8835 Views

Differentiate y=e^(x^2+2x)

For this question the chain rule should be used, the chain rule is that dy/du*du/dx=dy/dx. If we say u=(x 2 +2x) and therefore y=e u Then du/dx=2x+2 and dy/du=e u. Then dy/du*du/dx= (2x+2)e u , then we can s...
DF
Answered by Duncan F. • Maths tutor
15581 Views

How do you differentiate 2^x?

We can differentiate this implicitly by writing the question as:y = 2 x Then we take the log of both sides:ln(y) = ln(2 x )Using the rules of logartithms this can be written as:ln(y) = x ln(2)Now we can diff...
AC
Answered by Alex C. • Maths tutor
16101 Views