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This is an easy one as long as you remember the important equation y = mx + c. I can't express how important it is for you to learn that equation.

Step one: find y. Do this by taking 3x away from b...

Unlike a straight line, the gradient of a curve is not a constant i.e. not one single number. To find the gradient of a curve, you different the equation of the curve. To find the gradient at a specific p...

First, we choose u=sin(x),v'=exp(x). Using differentiation and integration of standard exponential and trigonometric functions => u'=cos(x),v=exp(x). From this we use the formula for integration by par...

Differentiate by multiply by the power and then minus 1 from the power. Use the rule: y= ax^b -> dy/dx = abx^(b-1)

dy/dx = 3 x 2x^(3-1) + -1 x 2x^(-1-1) + 0 dy/dx = 6x^2 - 2x^-2

Use the method of integration by parts. uv-integral(v.du/dx). Make u equal to ln(x) and dv/dx equal to 1. Therefore v=x and du/dx=1/x. Hence uv=xln(x). And v.du/dx=x/x=1. Substituting these into the 'by p...