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Popular >

derivative of (sqrt(81+x^2)/3+(15-x)/5)

Solution

\frac{d}{d x} (\frac{81 + x ^{2}}{3} + \frac{15 - x}{5})

Solution

\frac{x}{3 81 + x ^{2}} - \frac{1}{5}

Solution steps

\frac{d}{d x} (\frac{81 + x ^{2}}{3} + \frac{15 - x}{5})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{81 + x ^{2}}{3}) + \frac{d}{d x} (\frac{15 - x}{5})

\frac{d}{d x} (\frac{81 + x ^{2}}{3}) = \frac{x}{3 81 + x ^{2}}

\frac{d}{d x} (\frac{15 - x}{5}) = - \frac{1}{5}

= \frac{x}{3 81 + x ^{2}} - \frac{1}{5}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (sqrt(81+x^2)/3+(15-x)/5) ?
The derivative of (sqrt(81+x^2)/3+(15-x)/5) is x/(3sqrt(81+x^2))-1/5
What is the first derivative of (sqrt(81+x^2)/3+(15-x)/5) ?
The first derivative of (sqrt(81+x^2)/3+(15-x)/5) is x/(3sqrt(81+x^2))-1/5