If [math]t=g\left(x\right)[/math] and [math]\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)[/math] , the chain rule says that [math]\left(f\circ g\right)'=\frac{d}{dx}f\left(g\left(x\right)\right)=\frac{d}{dt}f\left(t\right)\cdot\frac{d}{dx}g\left(x\right)[/math]. [br]Experiment below with various inner functions [math]g[/math] and outer functions [math]f[/math] .