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Integrate 4x^3 + 6x^2 +4x + 3

Each term is integrated according to the formula: ax b --> (a/(b+1))x (b+1) A constant k integrates to kx Since this is indefinite integration, an additional term of +c must be added to the expression. Th...
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Answered by Emma H. • Maths tutor
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Differentiate y = 2x^3 + 6x^2 + 4x + 3 with respect to x.

Each term is differentiated according to the formula: y = ax b --> dy/dx = b*ax (b-1) Constants differentiate to zero. Therefore in this example: dy/dx = 6x 2 + 12x + 4
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Answered by Emma H. • Maths tutor
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Find the gradient of a curve whose parametric equations are x=t^2/2+1 and y=t/4-1 when t=2

Remember that the gradient of a curve is expressed as dy/dx. This can be solved by using the chain rule: dy/dx = dy/dt*dt/dx. The dt in the denominator of the first term, and the numerator of the second term...
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Answered by Abigail S. • Maths tutor
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Q: How to solve the simultaneous equations 3x+2y=7 and 5x+y=14

When solving simultaneous equations you are aiming to use both equations together to find out the value of x and y for values that with ‘fit’ in each equation. 3x + 2y = 7 5x + y = 14 If we subtract these eq...
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Answered by Katherine M. • Maths tutor
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Make x the subject of the equation y = {2(1+x)}/(3x+1)

This is an A* grade extension GCSE maths question on rearranging equations. The question is asking us to find an equation that would represent x . In the question this x appears on the denominator (bottom ha...
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Answered by Katrina G. • Maths tutor
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