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Maths
A Level

Why is the derivative of x^2 equal to 2x?

Differentiation is finding the slope of a graph; how steep it is at some point. In this case, we want to find out how steep the graph of x^2 is. To do this, we could look at the slope between two points o...

LH
Answered by Lawrence H. Maths tutor
15432 Views

How would I find the approximate area enclosed by the expression e^x*sin(x)*x^3 on an infinite scale?

The area under a curve is analytically calculated using the integral of the function. The integral of the function above could be calculated using integration by parts twice, considering that 3 functions ...

MW
Answered by Matthew W. Maths tutor
3022 Views

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 integrat...

CF
Answered by Christian F. Maths tutor
3591 Views

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...

GG
Answered by Gouri G. Maths tutor
7444 Views

A line L is parallel to y=4x+5 and passes through the point (-1, 6). Find the equation of the line L in the form y=ax+b . Find also the coordinates of its intersections with the axes.

Since L is parallel to y=4x+5 we know that the two lines have the same gradient. The gradient of a line in the form y=ax+b has is a, which means the gradient of y=4x+5 is 4, so L is y=4x+b and we just nee...

MM
Answered by Matt M. Maths tutor
11495 Views

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