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The gradient of a line in the form y = ax + b, where a and b are some numbers, is the number a . So we need to get the equation 3x + 5y = 7 into the above form, with y on one side on its own! We first move t...

First we want to calculate the derivative of y. To do this we use the product rule:If we rewrite y as y = uv, then dy/dx = v du/dx + u dv/dx.Here, we have u = x and v = cos(x).That means du/dx = 1 and dv/dx ...

As soon as you see a question asking you to integrate the square of sin, cos or tan, your first approach should be to use trigonometric identities and double angle formulas . For sin 2 (X), we will use the c...

When integrating a long chain of functions, we can integrate each term seperately and combine them. Let us now integrate:∫21x 6 dx = 21∫x 6 dx. Using the Power Rule [∫x a dx = (x a+1 /a+1)], we can say that ...

Write as y=uv u=x v=e x du/dx=1 dv/dx=e x Using the product rule, dy/dx=v du/dx + u dv/dx So dy/dx=e x (1)+x(e x )=e x (1+x)