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Differentiate x^2 from first principles

Differentiation is about finding gradients of functions. With straight lines we take the "rise of run" - the change in y over the change in x. With curves e.g. f(x) = x^2 we need to use the same...

Answered by • Maths tutor

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y is inversely proportional to d^2 and when d = 10, y = 4. d is directly proportional to x^2 and when x = 2, d = 24. Find a formula for y in terms of x. Give your answer in its simplest form.

Firstly, find proportionality equation between the two variables. This should be shown as d = kx^2 and y = b/d^2.Solve to find constants of proportionality of a=6 and b=400. Eliminating for d, find that y...

Answered by Jiangying (Susan) C. • Maths tutor

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How would you differentiate between the hypotenuse, opposite and the adjacent in a triangle?

Firstly, in a right angled triangle, the side opposite the right angle is always the hypotenuse which is the longest side in a right angle triangle. Secondly, the side opposite the given angle is your opp...

Answered by Jenny C. • Maths tutor

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How can I calculate the standard deviation of a data set?

The formula for the variance of a data set can be easily remembered by this catchy phrase: 'The mean of the squares minus the square of the mean'. The standard deviation is equal to the square root of the...

Answered by Robin M. • Maths tutor

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∫ x^3 *ln(2x) (from 2->1) can be written in the form pln 2 + q, where p and q are rational numbers. Find p and q.

Firstly I would think about how I could integrate this. In this case you would need integrate by parts. I use LATE to decide which value is u and v' which stands for Log,Algebra,Trig,Exp. Which ever one a...

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