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First we will differentiate y to find dy/dx= 4x³-16x. Stationary points exist at dy/dx=0 so we set 4x³-16x=0 and solve for x. x(4x²-16)=0. So x=0 or 4x²-16=0. I...

First remember that a parametric curve z = (x(t), y(t)) can be differentiated using the following formula (derived using the chain rule): dz/dt = (dy/dt)/(dx/dt). We should now find dy/dt and dx/dt (which...

I have written "… " where I would imagine the student is replying. I have then provided prompts assuming that the student did not come up with the answer straight away. Integration can ...

When differentiating a composite function y = (4x²-1)³ , the chain rule needs to be used.
The chain rule is dy/dx= dy/du x du/dx
In this instance we need to assign u and y ...

log₃(81) = 4 , log₂(32) = 59/log₂(x) = log₂(x)9 = (log₂(x))²3 = log₂(x) , -3 = log₂(x)x = 8 , x = 1/81 mark per line...