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Maths
A Level

integrate cos(2x) + sin(3x)

the differential of cos(x) is -sin(x). the differential of cos(2x) is -2sin(2x). you can think of it as differentiating what is in the bracket and putting that in front of the -sin(2x). when differentiati...

Answered by Ajay D. • Maths tutor
6672 Views

differentiate x^2 + 7x + 4

To differentiate you must times by the power then take one away from the power. Therefore x^2 + 7x + 4 would differentiate to become 2x + 7. The generic rule for differentiation can be written as dy/dx (x...

Answered by Ajay D. • Maths tutor
3650 Views

How can do you factorize the equation x^2+6x+8

Here, we see that the term in x in the equation is 6, so we start by looking for a perfect square where the second term would be 6 : we get 6/2 = 3 so we try (x+3)2. However, (x+3)2 = x

Answered by Marine S. • Maths tutor
2680 Views

Differentiate with respect to x, x^2*e^(tan(x))

Use the product rule: d/dx(uv) = uv' + u'v, with u = x^2 and v = e^(tan(x)), so that u' = 2x and v' = sec^2(x) * e^(tan(x)), and so the answer is 2x * e^(tan(x)) + x^2 * sec^2(x) * e^(tan(x)) .

Answered by Jakub H. • Maths tutor
4551 Views

Using partial fractions, find f(x) if f'(x)=5/(2x-1)(x-3)

First step: partial fractions 5/(2x-1)(x-3) 5=A(x-3)+B(2x-1) A=0 when x=3, so B=5/(2x3-1)=1 B=0 when x=1/2, so A=5/(0.5-3)=-2 So f'(x)=1/(x-3)-2/(2x-1) Second step: Integration f(x)= (integral)(1/(x-3))dx...

Answered by Jasmin F. • Maths tutor
4379 Views

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