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Talk about the relation between differentiability and continuity on a real function and its derivative.

In a real 2-Dimensional function f(x) on the X-Y plane, we have the following relations between these concepts: i) f'(x) is continuous if and only f(x) is differentiable; in fact, the continuity of f'(x) ens...
MM
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Can you explain where the "Integration by parts" formula comes from?

Sure. If you remember how to calculate d/dx(uv) then you can understand how integration by parts works. d/dx(uv) = u(dv/dx) + v(du/dx). we can re-arrange this: u(dv/dx) = d/dx(uv) - v(du/dx). Now integrating...
CF
Answered by Christian F. • Maths tutor
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Find the derivative of the curve e^(xy) = sin(y)

First we have to identify that implicit differentiation is used to solve this question. We can differentiate the first the LHS first, by using the chain rule, we know that the differentiation of e^(xy) is e^...
GG
Answered by Gouri G. • Maths tutor
8611 Views

Differentiate (2a+3)^5/2 with respect to a

Let u=2a+3, therefore du/da=2. Let y=u^5/2, therefore dy/du=5/2(u)^3/2 Hence dy/da=du/da*dy/du=2(5/2)*u^3/2=5u^3/2
GT
Answered by George T. • Maths tutor
4665 Views

A pizza has a radius of 12cm. Calculate the area of the pizza in cm² , giving your answer as a multiple of π.

So for this question you would need to know the formula for the area of a circle. This is Area = πr^2. In this formula, r = the radius. We are given the radius in the question. So all we need to do is put ou...
JH
Answered by Jess H. • Maths tutor
7572 Views