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We start by expanding out the double trigonometric terms (sin(2a)) using the double angle formula, giving us: [2sin(a)cos(a)] / [1+cos^2(a) - sin^2(a)]. Next we spot that on the denominator (bottom half o...

The definite integral gives the value of the area bounded between the curve at the given limits, and the x-axis (if we are integrating with respect to x!) If this value is negative, it means that the area...

using the product rule

product rule is dy/dx=v.du/dx+u.dv/dx

let u = x^2 and v = cos(x)

du/dx=2x

dv/dx = -sin(x)

so dy/dx=2xcos(x)-x^2sin(x)

My exact explanation would depend on the students level of understanding. The following answer assumes a basic understanding of differentiation and equations of lines; a) Gradient of tangent is equal to g...

To differentiate x^x, we first let y = x^x. (Note that x^x is not in the form x^c w...