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y = 4x²(x+3)⁵ . Use the product rule to find the first derivative of the curve, 8x(x+3)⁵ + 20x²(x+3)⁴ , and substitute x = -1 to find the gradient at...

You should use the product rule when you have a function f(x), which you can't differentiate straight away. But which can be written in the form f(x)=g(x)h(x), where g(x) and h(x) are functions that you d...

Using one of the equations we express either x in the form of y, or y in the form of x. We then put this expression of x/y into the other equation. This allows us to calculate the numerical values of both...