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First let y=ln(x). Recall that the exponential function, e x , is defined as the inverse of the logarithmic function, ln(x). To make x the subject of the formula, use the inverse function exp. This gives tha...

Let's start with the definition of sin( x ) and cos( x ). We're going to use t rather than x here to avoid confusion, but the idea is exactly the same. Take a unit circle - that is, a circle with centre (0,0...

To sketch a polynomial function (a polynomial is a function involving powers of x, for example y = x 3 + 2x 2 - 13x + 10): 1. Start by differentiating the function to find its turning points (where the first...

Step 1: To differentiate an equation there is a simple rule to follow. For y=ax n dy/dx=anx n-1 . so for an example y=x 3 , dy/dx=3x 2. Therefore we just apply this rule into our equation. Step 2: Break the ...

When you are faced with an integral which is a product, such as x.cos(x) , you may be able to integrate it by parts. The statement of the integration by parts is that: ∫u(dv/dx)dx = uv-∫v(du/dx)dx So if you ...