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The chain rule is used to differentiate when there is a function within another function. For example y=(4x+6)^0.5, y=(x+1)³The general formula for the chain rule is dy/dx= dy/d...

First the student needs to differentiate the function to find dy/dx = 2x-6At dy/dx = 0, we know the curve is stationary. Now we can work out the x value such that x = 3Put x=3 back into the original equat...

cos(2y)= (cos(y))^2 - (sin(y))^2 identitynow consider identity (cos(y))^2+(sin(y))^2=1by rearranging this to (cos(y))^2 - 1 = - (sin(y))^2 we can now substitute it into our first identity to obtaincos(2y)...

This is an equation laid out in terms of the natural logarithm, which essentially is the reverse function of e^x . From this equation we need to find a solution for x =? Since we know that this ...

y=3x⁴-8x³-3
Let's say we want to calculate dy/dx. For a term Axⁿ, the differential with respect to x is Anx^n-1. For a constant value, we can say t...