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First let a = b = x such that:          

          cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

becomes:

          cos(x + x) = cos(x)cos(x) - sin(x)sin(x)

Leading to:

     ...

Note that this property is the definition of an odd function, or draw a sketch of what this looks like in general about the horizontal axis. E.g. f(x)=sin(x) which has the expansion f(x)=x-((x^3)/3!)+((x^...

Find the derivative of f(x)=x³ sin(x).

To do this calculation we need to use the product rule of differentiation: if f(x)=u(x)v(x), then the derivative is f'(x)=u'(x)v(x)+u(x)v'(x). In o...

First of all we are asked to differentiate the function. This can be easily done by multiplying the coefficient of x by its exponent, and then decreasing the exponent by one. Therefore, dy/dx=3x^2+4x We a...

Here you are being asked to differentiate. When differentiating, you times the value of x by its power and then subtract 1 from the power. So for this question you times 6x^(1/2) by 1/2 and then subtract ...