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Differentiate y=(x^2 + 2x)cos(3x)

Here we need to use the product rule in order to differentiate as we have two functions involved that are being multiplied together. Therefore we use the formula:dy/dx = u dv/dx + v du/dxFirst let u=(x^2 ...

Answered by Katie B. • Maths tutor

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Show that x^2 +6x+ 11 can be written as (x+p)^2 +q

x²+6x +11this is a quadratic so we try to factorise it. x²+6x can be turned into (x+3)²-9 and we plus the 11 from the beginning so the final answer should look like (x+...

Answered by Abdullahi M. • Maths tutor

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Solve the following simultaneous equations: y-3x+2=0, y^2-x-6x^2=0

(1) y-3x+2=0
(2) y²-x-6x²=0
Using (1): y=3x-2
Sub y value into (2): (3x-2)²-x-6x²=0
Expand the brackets: 9x²-13x+4-x-6x

Answered by Phoebe A. • Maths tutor

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Prove that cos(4x) = 8(cos^4(x))-8(cos^2(x)) + 1

cos(4x) = cos(2(2x)) = 2(cos^2(2x)) - 1 = 2 (cos^2(x) - 1)^2 - 1 = 8(cos^4(x)) - 8(cos^2(x)) + 1

Answered by Harry T. • Maths tutor

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How would you integrate (4x+1)^1/3 ?

Firstly, increase the power outside the brackets by 1 and divide the whole thing by the new power. This gives 3/4(4x+1)^4/3Next, divide the whole thing by the derivative of the bracket. The deri...

Answered by Nicholas G. • Maths tutor

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