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How would you go about integrating a function which has an exponential and a cos/sin term?

For this type of integral you would need to use integration by parts twice. Remember this is where the integral of u*(dv/dx)=uv-(integral with respect to x)(v*(du/dx)). For example let's say you need to inte...
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Answered by Luke R. • Maths tutor
4407 Views

I can differentiate exponentials (e^x), but how can I differentiate ln(x)?

[Differentiate y = ln(x)] This is an example of many situations in maths where you need to solve something that is similar to what you can solve, but not in its current form. A good idea, then, is to see wha...
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Answered by Adam L. • Maths tutor
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Solve the equation 3x^2/3 + x^1/3 − 2 = 0

Let u = x^1/3 The equation can therefore be written as: 3u^2+u-2=0 This can be factorised to: (3u-2)(u+1)+0 Therefore: u = 2/3 or u = -1 OR x^1/3 = 2/3 or x^1/3 = -1 So: x = (2/3)^3 or x = (-1)^3 x = 8/27 or...
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Answered by Namita H. • Maths tutor
10295 Views

How do you differentiate using the chain rule?

In order to differentiate using the chain rule,you first need to know the chain rule. Chain rule : dy/dt * dt/dx = dy/dx. It is basic multiplication to get rid of the common factor of 'dt' in both equations ...
NG
Answered by Niha G. • Maths tutor
4002 Views

A curve has equation y^3+2xy+x^2-5=0. Find dy/dx.

To find the derivative of this, we must differentiate each term with respect to x. This implies d/dx(y^3+2xy+x^2-5=0). We can differentiate each term seperately so d/dx(y^3+2xy+x^2-5=0) is equal to d/dx(y^3)...
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Answered by Matthew C. • Maths tutor
5537 Views