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Find the gradient of the function f(x,y)=x^3 + y^3 -3xy at the point (2,1), given that f(2,1) = 6.

Firstly, establish that the correct method to do this is via differentiation: specifically implicit differentiation. To find the gradient, we need to find dy/dx. The differential with res...

Answered by Daniel D. • Maths tutor

5718 Views

If f(x) = sin(2x)/(x^2) find f'(x)

As f(x) is in the form of u(x)/v(x) we can apply the rule that f'(x) = (u'(x)*v(x) - v'(x)*u(x))/(v(x)²), pulled from the C3 formula booklet.
If u(x) = sin(2x) then u'(x) = 2cos(2x).
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Answered by Leo R. • Maths tutor

3623 Views

The function f (x) is defined by f (x) = (1-x)/(1+x), x not equal to -1. Show that f(f (x)) = x. Hence write down f ^-1 (x).

f(f (x) )= f( (1-x)/(1+x) ) = (1-(1-x)/(1+x))/(1+(1-x)/(1+x))where you replace x by (1-x)/(1+x). Multiply the top and bottom of the fraction by (1+x) to get ((1+x)-(1-x))/((1+x)+(1-x)) which simplifies t...

Answered by Sarah P. • Maths tutor

11545 Views

What should I focus on when analysing the use of symbolism and imagery in W.B Yeats's 'Wild Swans at Coole'?

When analysing the use of symbolism in a poem, you should search for a central motif, the meaning of which seems to bear more weight that what may be literally construed upon first reading. In the case of...

Answered by Timothy M. • English tutor

4216 Views

What is the normal distribution and how do I use it?

The normal distribution is a distribution we can use when we know the mean and the standard deviation of a population, to work out probabilities that a certain even will occur.
The main properties of...

Answered by Chantelle C. • Maths tutor

3397 Views