CoCalc Public FilesSAGEWS / 10-diffrules.sagews

## The Rules of Differentiation

### Constant Rule

\begin{align}\mbox{If }f(x)=a\mbox{ and }a\mbox{ is a real number, then }f'(x)=0.\end{align}

### Constant Multiple Rule

\begin{align}\mbox{If }f(x)=ax\mbox{ and }a\mbox{ is a real number, then }f'(x)=a.\end{align}

### Power Rule

\begin{align}\mbox{If }f(x)=x^n\mbox{ and }n\mbox{ is a real number, then }f'(x)=nx^{n-1}.\end{align}

### Product Rule

\begin{align}\mbox{If f and g are differentiable at x, then }\left(f\cdot g\right)'(x)=f(x)g'(x)+g(x)f'(x)\end{align}

### Quotient Rule

\begin{align}\mbox{If f is the quotient g(x)/h(x) and h(x) ≠ 0, then } f'(x)=\frac{g'(x)h(x)-g(x)h'(x)}{\left[h(x)\right]^2}\end{align}

### Chain Rule

\begin{align}\mbox{If g is differentiable at x and f is differentiable at g(x), then }\left(f\circ g\right)'(x)=f'(g(x))g'(x)\end{align}

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