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dy/dx=2x + 2

Turning point is where dy/dx=0, so when x = -1

When x=-1, y=0.

d^2y/dx^2=2 > 0 therefore minimum.

3e^3x + (9x)e^3x This is a good question because it involves the use of both the chain and product rules of differentiation, as well as the differential of e (all of which occur frequently in Maths A-leve...

Firstly, we may simplify the expression by factoring out any constants. In this case 5 can be factored out. 

5 ∫ cos(3x-1) dx 

For the integrand cos(3x -1), we can use a simple u-substitutio...

The chain rule is a rule of differentiation that states: (f(g(x))'=f^'(g(x))g'(x)

In effect, the chain rule allows us to split up a complicated equation ...

Understand the question:

'w.r.t' stand for 'with respect to', so the qestions is asking for the dericative and integral to be calcuated in terms of x - so find dy/dx and (integral sign) y dx...