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We would do this by differentiating everything individually so to differentiate x² we multiply the x² by the power which is 2 and then take the power down by 1 to make 2x. To differe...

Let a=60 and b=300.

Then cos(a)=cos(60)=0.5 and cos(b)=cos(300)=0.5, therefore cos(a)=cos(b).

Then sin(a)=sin(60)=sqrt(3)/2 and sin(b)=sin(300)=-sqrt(3)/2, therefore sin(a)=sin(b) is incorre...

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...