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How do I differentiate y=x^x?

y=x^ x To find the differential, dy/dx, logs of both sides must be taken: log(y)=log(x^ x ) Then using log rules, the power can be brought down, outside the log expression: log(y) = x log(x) This expre ssion...
PL
Answered by Pascal L. • Maths tutor
17299 Views

how to integrate by parts

If you aren't lucky enough to be told in the question, the first thing we have to do is know when we should you integration by parts. Well, like most things in maths this should become second nature to you w...
TM
Answered by Tim M. • Maths tutor
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How do I integrate terms with sin^2(x) and cos^2(x) in them? For example integrate (1+sin(x))^2 with respect to x

As you will be aware, it is not easy to directly integrate terms involving sin^2(x) and cos^2(x), so we use a substitution to turn them into something which we can integrate. From the double angle formula fo...
MH
Answered by Michael H. • Maths tutor
19000 Views

How do I add two fractions? (plus example)

Adding (and subtracting) fractions is more difficult than multiplying them because we need to make sure that the denominators (bottom numbers) are equal in both fractions. To do this, we may need to change t...
JB
Answered by Jenny B. • Maths tutor
5548 Views

How do I expand (x+a)(x+b)? (plus example)

The key to understanding expanding brackets is to understand that we need to multipy EVERYTHING in the first bracket by EVERYTHING in the second bracket. We can think of the calculation (x+a)(x+b) as x(x+b) ...
JB
Answered by Jenny B. • Maths tutor
16953 Views