What formula do we need, in addition to: ddx(xn)=nxn−1 ddx(cu)=cdudx ddx(u1+u2+…+un)=du1dx+du2dx+…+dundx to differentiate rational functions?

Resolved: "What formula do we need, in addition to:..."

Secondary
Calculus and Analysis
Precalculus
Transformations of functions

Khadija Wells

Answered question

2021-06-01

What formula do we need, in addition to:

\frac{d}{d x} (x^{n}) = n x^{n - 1}

\frac{d}{d x} (c u) = c d \frac{u}{d x}

\frac{d}{d x} (u_{1} + u_{2} + \dots + u_{n}) = d \frac{u_{1}}{d x} + d \frac{u_{2}}{d x} + \dots + d \frac{u_{n}}{d x}

to differentiate rational functions?

Answer & Explanation

Tasneem Almond

Skilled2021-06-02Added 91 answers

Since rational function include fractions, we need the following formula for differentiating rational functions:

\frac{d}{d x} \frac{f (x)}{g (x)} = (\frac{(d \frac{f}{d x}) (x) g (x) - f (x) (d \frac{g}{d x}) x}{g^{2} (x)}

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