Fluency exercise

# I can see $u$! Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

## Problem

If $u=2x+1$ and $y=u^3$ what is $y$ as a function $x$?

Working backwards, if $y=(2x+3)^{-2}$, how could you express $y$ as a function of $u$ where $u$ is a function of $x$?

If you also wanted to work out $\dfrac{dy}{dx}$, how would this affect your choice of $u$?

Take a look at the functions in the table below.

Write $y$ as a function of $u$ where $u$ is a function of $x$ so that you can use these to find $\dfrac{dy}{dx}.$

You may be able to do this in more than one way.

 $y=(5-2x)^3$ $y=\sqrt{3x-1}$ $y=\dfrac{5}{\sqrt{x}}$ $y=9x^2-6x+1$ $y=e^{5x}$ $y=\ln{3x}$ $y=\dfrac{1}{x^2+4x+4}$ $y=e^{x+4}$ $y=\ln{x^2}$ $y=\cot x$ $y=x$ $y=\ln{x^2}+\ln{8x}$ $y=\sin x^2$ $y=\tan x (\sec^2 x-1)$ $y=\tfrac{1}{2}(1-\cos 2x)$