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Let A=7x and B=3x( From the formulae we know that sinxcosx= 1/2(sin(A+B)+sin(A-B))So if we replace A=7x and B=3x in this equation: 1/2(sin(7x+3x)+sin(7x-3x))= = 1/2 (sin(10x)+sin(4x))Now we just integrate...

Let u=6x-3 , then y=u^-0.5hence, du/dx=6 and dy/du= -0.5u^-3/2then, as dy/dx =dy/du * du/dx dy/dx=(-0.5u^-3/2 )*6= -3(6x-3)^-3/2substitute x=2 to give the required value required value : -1/9

In this question we will use the fact we know a straight line can be written in the form (y-y₁)=m(x-x₁). Where m is the gradient and (x₁,y₁) is a point on the l...

Derivatives can be used to work out rates of change of non-linear systems which are encountered everyday. Moreover derivatives allow us to describe the shape of a function.

equation of a circle: (x - a)^2 + (y - b)^2 = r^2, where the circle has centre (a, b) and radius r.
Let's draw the diagram, where (x, y) is some point on the circle, which for ease we'll call P, and...