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As V=(h⁶+16)^1/2 -4, the chain rule can be used to calculate dV/dh.

dV/dh=3h⁵(h⁶+16)^-1/2

h=2 can be su...

Roots = where line touches x-axis. Set equation equal to 0 as y=0 at the x-axis. Now we need to solve for the x values at which y=0. Quadratic is now 0=x^2+5x+6. Factorise quadratic: 0=(x+3)(x+2). Now you...

f'(x)= 3x^2+1/3x^(-2/3)

To differentiate you need to multiply the coefficant of the x dependent terms by the powers and then the power of x goes down by one. 

For example: differentiate f(x)...

First, expand the brackets. This will give us 10x^3/2 - 20x. Now to integrate this expression we have to increase the power of each term by one and then divide them by the number which becomes the new pow...

First we need to find the derivatives of x and y in terms of t. dx/dt can be found using the chain rule. Differentiating the inside of the bracket gives us 2. Multiplying the outside gives -2sin(2t) (Deri...