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Maths
A Level

What is the general rule for differentiation?

In differentiation you multiply the coefficient of the subject (what the value is multiplied by e.g. 3 is the coefficient of 3x6) by its exponent (the power that the value is raised to e.g. ...

Answered by Oisin B. Maths tutor
3357 Views

How would you differentiate f(x)=3x(2x-1)^2

This question is really straight forward

By using the Chain rule: f'(x) = uv' + u'v.

let u=3x, so u'=3

let v=(2x-1)^2, so v'=2x2(2x-1)=8x-4

Now, ...

Answered by Ruihang Z. Maths tutor
5710 Views

Integrate 1/(5-2x) for 3≤x≤4

You must be careful with these sorts of questions as although 1/(5-2x) is equivalent to (5-2x)^-1, when you integrate you would add one to the power and divide by the new power. But if you were to add one...

Answered by Emily-Louisa S. Maths tutor
6232 Views

Using the addition formula for sin(x+y), find sin(3x) in terms of sin(x) and hence show that sin(10) is a root of the equation 8x^3 - 6x + 1

First we state the formula for sin(x+y)

sin(x+y) = sin(x)cos(y) + cos(x)sin(y)

Letting y = 2x

sin(x+2x) = sin(x)cos(2x) + cos(x)sin(2x)

Now sin(2...

Answered by Kyle R. Maths tutor
21001 Views

Using Integration by Parts, find the indefinite integral of ln(x), and hence show that the integral of ln(x) between 2 and 4 is ln(a) - b where a and b are to be found

Using integration by parts, we can re-write the integral of ln(x) as (xln(x) - int(x(1/x))) = x*ln(x) - x

Therefore, evaluating between 2 and 4 gives us (4ln(4) - 4) - (2

Answered by Kyle R. Maths tutor
3325 Views

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