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y=sin(x²) + e^x Firstly we need to differentiate. dy/dx = 2xcos(x²) + e^x using the chain rule Notice the gradient at x = sqrt(pi) is found when we sub x into dy/...

This question requires integration by parts, using the formula:

Integral(u dv) =  u v - integral(v du) 

This is applied to find the integral of Ln(x) by writing Ln(x) as 1 * Ln(x), u is then...

With differentiation we should always begin with the "times by the power and take one from the power" rule. For example, to differentiate ax^b --> (a x b)x^(b-1)

So...

x=-1/7 or -1/3

y=-3/7 or 1/3

Being able to find partial fractions is very useful for complex algebraic fractions that cannot be intergrated in their current form. Breaking it down into a sum of it's partial fractions gives two (or mo...