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Firstly, simplify the numerator by factorising the quadratic, to give a numerator of (3x+2)(x-1). Now, divide through by (x-1), to give (3x+2).

The chain rule can be used to find more complex derivatives.For example, in the case of: y = (5x + 2)⁵To find the derivative in the ordinary fashion, one would need to expand the brackets to:y=...

We need the equation in the form (x+a)(x+b)=0. The numbers in the brackets (a and b) must multiply together to get the constant at the end of the equation, in this case 12. The numbers (a and b) must add ...

Let’s say we’re given the equation y=(2x-6)^4we would know how to differentiate x^4, therefore we can take the substitution u=2x-6 to give us the equation y=u^4we then differentiate this equation (dy/du) ...

Using the product rule H(X) = f(x)*g(x) and H'(X) = f'(x)*g(x) + f(x)*g'(x) Where, in this case f(x) = x³ and g(x) = e^x We can easily determine the derivative of the above function.f...