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To answer this question we require the chain rule, which states that dy/dx=(dy/du)*(du/dx)

To use this formula in our question, we can let y=ln(sin(3x))=ln(u) where u=sin(3x)

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First, write the line in vector form r=(1 1 1) + t(1 2 -1). Consider a point P on the line such that the line connecting P and A is perpendicular to L. The vector P->A is (2 3 4) - (1 1 1) - ...

This is an algebraic fraction. There is more than one way of solving this expression, but the simplest is to factorise both the top and the bottom quadratic expressions.Firstly we shall simplify the top e...

A simple way to differentiate an equation with respect to x is to reduce each x components power by one and multiply each x component by their original power.

Looking at the equation y = ...

A good approach to solve this is to use the chain rule of differentiation. The chain rule states: dy/dx= (dy/du)*(du/dx).

In this case let u = 1+3x, so y = u^2.

Then dy/du =...