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a) Firstly, differentiate x and y with respect to t. 

Giving you dx/dt = 1/t       and dy/dt = 12t²

dy/dx is found using the chain rule:

Calculate the gradient of the function y=x^2+6x when y=-9

For a curve of gradient dy/dx = (2/(x^2))-x/4, determine a) d^2y/dx^2 b) the stationary point where y=5/2 c) whether this is a maximum or minmum point and d) the equation of the curve

Find ∫ ( 2x^4 - 4x^(-0.5) + 3 ) dx