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If y = (4x^2)ln(x) then find the second derivative of the function with respect to x when x = e^2 (taken from a C3 past paper)

The first thing to recognise is that this function is a product of two functions: namely, 4x^2 and ln(x), thus we must employ the product rule in order to find the solution. As you may recall, the product ru...
CS
Answered by Caspar S. • Maths tutor
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Find the exact gradient of the curve y=ln(1-cos2x) at the point with x-coordinate π/6

This is a past paper question for an A level OCR MEI paper for Maths.We need to find the gradient of the curve so we know right away that we need to use differentiation.The equation y = ln(1-cos2x) is diffic...
CH
Answered by Catherine H. • Maths tutor
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How can I derive an equation to find the sum of an arithmetic sequence?

This isn't a requirement of many courses but understanding and proving mathematics has order is what makes mathematics unique and enjoyable to many. Imagine the sum of a sequence with n terms, denoted S n , ...
RH
Answered by Rhys H. • Maths tutor
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How to integrate by parts

Sometimes while integrating, we may come across an expression that is not a polynomial, and thus we cannot use the convenient power rule to integrate. Consider the function y=xcos(x). It is not immediately c...
DL
Answered by Dennis L. • Maths tutor
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Differentiate y = 4ln(x)x^2

So we want to differentiate y = 4x 2 ln(x) with respect to y. For this we need to use the product rule. The product rule is D {f(x)g(x)} = f(x)g'(x) + g'(x)f(x) We can therefore make f(x) = 4x 2 and g(x) = l...
BP
Answered by Beth P. • Maths tutor
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