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Differentiate y = 15x^3 + 24x^2 + 6 with respect to x.

To differentiate y with respect to x, you have to multiply each x term by their respective power and then decrease their power by one. For example, 4x 2 differentiated is 2 x 4x 2-1 = 8x. So, splitting this ...
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Answered by Dominic M. • Maths tutor
4307 Views

What the integral of e^2x*x? (limits 0,1)

Whenever you see an integral with a product as the integrand, check if integration by parts works. That is, Int(v(x)*u'(x)) = u(x)v(x)-int(u(x) v'(x)) So you should see that its easier to call v(x)=x and u'(...
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Answered by Oliver O. • Maths tutor
4624 Views

A shop trying to sell a laptop reduces its price by 7% at the very end of each week, from an initial price of £600. If you have £365 to spend, how many weeks must you wait until you can buy the laptop?

This is a simple question, but it's important to not get confused when thinking about how the laptop's price gets reduced. We know the price starts at £600, and that it goes down by 7% each week. If somethin...
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Answered by Kiavash S. • Maths tutor
3619 Views

How do you find the stationary points on a curve?

Let y = f(x). The gradient of the tangent to the curve at a stationary point is equal to 0. To find an equation for the gradient of the curve, differentiate f(x) to get dy/dx. Because we are looking for stat...
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Answered by Caroline M. • Maths tutor
4298 Views

Solve the simultaneous equations: x+y=2 , 4y²-x²=11

These equations would best be solved using the substitution method, in this case the easiest way would be substituting x. For the first equation we need to rearrange it to get x on one side so we have x=2-y....
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Answered by Waris P. • Maths tutor
6725 Views