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Further Mathematics
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How would you differentiate x^x?

To start off with, we have the expression y = x^x and we want to differentiate it. A clever way to do this would be to first remember implicit differentiation and start by taking the natural logarithm of ...

AD
2233 Views

Differentiate arctan(x) with respect to x

We can set arctan(x) = y. Remember that arctan(x) is the inverse of tan(x), so we can take the tangent of both sides to give: tan(arctan(x)) = x = tan(y). Tan(x) has the standard derivative of sec^2(x) (w...

SE
4647 Views

If y=(x^2)*(x-10), work out dy/dx

The question is pretty straightforward and asks you to find the derivative of y, which is a function of x. The most simple way to do this is to first eliminate the brackets and then derive. Thus we get y=...

MC
3538 Views

The curve C has equation f(x) = 4(x^1.5) + 48/(x^0.5) - 8^0.5 for x > 0. (a) Find the exact coordinates of the stationary point of C. (b) Determine whether the stationary point is a maximum or minimum.

Part a:f(x) = 4x1.5 + 48x-0.5 - 80.5Finding the gradient function, f'(x) = 6x0.5 - 24x-1.5At the stationary point, the gradient is zero, so f'(x) = 0...

SP
2588 Views

A curve is defined by the equation y = (x + 3)(x – 4). Find the coordinates of the turning point of the curve.

The turning point of a curve is the point at which it will turn, therefore, either the maximum or minimum point. Firstly, you need to expand out the brackets so the equation looks like a standard curve eq...

CM
2693 Views

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