# Look at the Chain Rule formula with a visual explanation of how it works: PS

Look at the Chain Rule formula with a visual explanation of how it works:
${\left(h\left(x\right)\right)}^{\prime }={\left(g\left(f\left(x\right)\right)\right)}^{\prime }={g}^{\prime }\left(f\left(x\right)\right)\cdot {f}^{\prime }\left(x\right)$
$g\left(f\left(x\right)\right)$-outside function
$\left(f\left(x\right)\right)$-inside function
${g}^{\prime }\left(f\left(x\right)\right)$-derivative of the otside at f(x)
${f}^{\prime }\left(x\right)$-derivative of the inside
Now, explain what happens in regards to calculating the derivative, if f(x) is also a composite function.
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Kathleen Ashton
Step 1
Let f(x) also be a composite function
$⇒f\left(x\right)=p\left(q\left(x\right)\right)$
$\therefore h\left(x\right)=g\left(f\left(x\right)\right)=g\left(p\left(q\left(x\right)\right)\right)$
$\therefore$ Using chain rule
${h}^{\prime }\left(x\right)={g}^{\prime }\left(p\left(q\left(x\right)\right)\cdot {p}^{\prime }\left(q\left(x\right)\right)\cdot {q}^{\prime }\left(x\right)$
$={g}^{\prime }\left(f\left(x\right)\right)\cdot {p}^{\prime }\left(q\left(x\right)\right)\cdot {q}^{\prime }\left(x\right)$