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[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...

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...

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 ...

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)...

To differentiate you bring the power down and multiply it by any coefficients (numbers in front of the xs) then subtract one from the power So x 3 becomes 3x 2 2x 2 becomes 2*2x 2-1 = 4x 4x becomes 4*1x 1-1 ...