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# The Rules of Differentiation

### Constant Rule
If $f(x)=a$ and $a$ is a real number, then

$f'(x)=0$.
### Constant Multiple Rule
If $f(x)=ax$ and $a$ is a real number, then

$f'(x)=a$
### Power Rule
If $f(x)=x^n$ and $n$ is a real number, then

$f'(x)=nx^{n-1}$.
### Product Rule
If $f$ and $g$ are differentiable at $x$, then

$(f*g)'(x)=f(x)g'(x)+g(x)f'(x)$
### Quotient Rule
If $f$ is the quotient $\dfrac{g(x)}{h(x)}$ and $h(x)≠0$, then

$f'(x)=\dfrac{g'(x)h(x)-g(x)h'(x)}{[h(x)]^2}$
### Chain Rule
If $g$ is differentiable at $x$ and $f$ is differentiable at $g(x)$, then

$(f\circ{g})'(x)=f'(g(x))g'(x)$

︡e3816b0c-e49c-48ca-bcae-534df0a5a90b︡︡{"done":true,"md":"# The Rules of Differentiation\n\n### Constant Rule\nIf $f(x)=a$ and $a$ is a real number, then\n\n$f'(x)=0$.\n### Constant Multiple Rule\nIf $f(x)=ax$ and $a$ is a real number, then\n\n$f'(x)=a$\n### Power Rule\nIf $f(x)=x^n$ and $n$ is a real number, then\n\n$f'(x)=nx^{n-1}$.\n### Product Rule\nIf $f$ and $g$ are differentiable at $x$, then\n\n$(f*g)'(x)=f(x)g'(x)+g(x)f'(x)$\n### Quotient Rule\nIf $f$ is the quotient $\\dfrac{g(x)}{h(x)}$ and $h(x)≠0$, then\n\n$f'(x)=\\dfrac{g'(x)h(x)-g(x)h'(x)}{[h(x)]^2}$\n### Chain Rule\nIf $g$ is differentiable at $x$ and $f$ is differentiable at $g(x)$, then\n\n$(f\\circ{g})'(x)=f'(g(x))g'(x)$"}
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<center>[Previous: Differentiability](Differentiability.sagews) | [To Main](Introduction.sagews)
︡d403c953-cb5d-4ffa-ac1d-0808b4c6bb8f︡{"done":true,"md":"<center>[Previous: Differentiability](Differentiability.sagews) | [To Main](Introduction.sagews)"}
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Collaborative Calculation and Data Science

colby

sagemath

The Rules of Differentiation

Constant Rule

Constant Multiple Rule

Power Rule

Product Rule

Quotient Rule

Chain Rule

Product

Resources

Company