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Given that y = (1 + 3x^2)^(1/3) , use the chain rule to find dy/dx in terms of x.

Take u = 1+3x 2 , this gives that y = u 1/3 . By the chain rule we have that dy/dx = dy/du * du/dx. By differentiating y = u 1/3 with respect to u gives dy/du = (1/3)u -2/3 . By differentiating u = 1 + 3x 2 ...
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Answered by Jasmine S. • Maths tutor
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Integrate f(x)=lnx

Integration by parts formula is given in all A level maths formula books however would be of use to memorise Formula: INT(uv')dx= uv- INT(u'v)dx Hint: write lnx as (1).lnxlet u=lnxhence u' = du/dx = 1/x let ...
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Answered by George N. • Maths tutor
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A curve has the equation y=3x^3 - 7x^2+52. Find the area under the curve between x=2 and the y-axis.

With a question like this. Firstly you have to read it, of course. But more importantly you have to understand what it is asking of you. So it is asking to find the area with boundaries at x=2 and the y axis...
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Answered by Calvin C. • Maths tutor
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How do you prove a mathematical statement via contradiction?

For a proof via contradiction , you would start by assuming the statement is actually false 1 (even if the given statement seems inherently correct, it is essential for the proof). Now that you have a basis ...
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Answered by Jake S. • Maths tutor
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Calculate dy/dx of the following equation: y = 3x^3 - 6x^2 + 2x - 6

dy/dx = 9x^2 - 12x + 2
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Answered by Ahanna N. • Maths tutor
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