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Here, we must first rearrange our equation so all x terms are on one side and all y terms are on the other. Multiplying both sides by dx and diving both by y^(1/2) gives us y^(-1/2)dy = sin(x/2)dx, which ...

To answer, we must be familiar with several trigonometric identities and expressions; first notice that tan(x)=sin(x)/cos(x). Now our function is a quotient of two functions of x that we can easily differ...

First we must find the gradient of the curve at the point (1, 4) - we do this by finding the derivative dy/dx, as we do to find any gradient. Differentiating the equation of the curve gives us that dy/dx ...

Integrating by parts requirez recognition that ln(x) is equal to ln(x) multiplied by 1. Making u equal to ln(x) should make the integration trivial. Differentiation is a simple use of the product rule and...

First, let's make y the subject of the equation.

Let's achieve this by having only y on the left hand side of the equation. To do this we need to minus 3x from both sides of the equation. This leav...