# Summary of Differentiation Rules

Differential Calculus #4: Rules of Differentiation

Tip: This isn't the place to ask a question because the teacher can't reply.

1 of 3 videos by Darshan Senthil

## Key Questions

• Power rule:
if $f \left(x\right) = {x}^{n}$ then $f ' \left(x\right) = n {x}^{n - 1}$

Sum rule:
if $f \left(x\right) = g \left(x\right) + h \left(x\right)$ then $f ' \left(x\right) = g ' \left(x\right) + h ' \left(x\right)$

Product rule:
if $f \left(x\right) = g \left(x\right) h \left(x\right)$ then $f ' \left(x\right) = g ' \left(x\right) h \left(x\right) + g \left(x\right) h ' \left(x\right)$

Quotient rule:
if $f \left(x\right) = g \frac{x}{h \left(x\right)}$ then $f ' \left(x\right) = \frac{g ' \left(x\right) h \left(x\right) - g \left(x\right) h ' \left(x\right)}{h \left(x\right)} ^ 2$

Chain rule:
if $f \left(x\right) = h \left(g \left(x\right)\right)$ then $f ' \left(x\right) = h ' \left(g \left(x\right)\right) g ' \left(x\right)$
Or:
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{du}} \cdot \frac{\mathrm{du}}{\mathrm{dx}}$

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