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Differentiate: y = 4x^3 - 5/x^2

To make this equation easier to differentiate it would be easier to write it using index rules as y = 4x^3 - 5x^-2 From here we can begin to differentiate: dy/dx = 3*4x^(3-1) - (-2)*5x^(-2-1) Then finally si...
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Answered by Chris B. • Maths tutor
8729 Views

Find the integral of xcosx(dx)

Firstly, let's split the equation "xcosx" into two parts to integrate them separately. 1) Let u=x and dv/dx=cosx 2)As the integral of x is 1, du/dx=1 3)To find v, we integrate cosx to get v=sinx Us...
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Answered by Amelia F. • Maths tutor
18122 Views

Rationalise the denominator of 25/sqrt(5)

In maths when we are asked to re express something we really only have 2 tricks. Multiply by 1, or add Zero. The hard part is finding how to express 1 or zero to suit the problem. For this one we should mult...
SO
Answered by Sean O. • Maths tutor
6659 Views

Find the indefinite integral tan(5x)tan(3x)tan(2x)

Noticing that tan(5x) = tan(3x+2x) we use the tan compound angle formula to find tan(5x) = (tan(2x)+tan(3x))/(1-tan(2x)tan(3x)) and thus tan(5x)tan(3x)tan(2x) = tan(5x)-tan(3x)-tan(2x). From then we can inte...
SO
Answered by Sean O. • Maths tutor
14560 Views

Factorise (x^2 +3x-18)=0, solving for x

To factorise and solve this equation we must put it into two brackets, instead of one, each with a single x term. As the is an x^2 term we know there must be an x in each bracket Because the number term at t...
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Answered by Rachael M. • Maths tutor
6477 Views