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Popular >

derivative of (s^6+1/s)^{5/2}

Solution

derivative of

(s^{6} + \frac{1}{s})^{\frac{5}{2}}

Solution

\frac{5 ( s ^{6} + \frac{1}{s} ) ^{\frac{3}{2}}}{2} (6 s^{5} - \frac{1}{s ^{2}})

Solution steps

\frac{d}{d s} ((s^{6} + \frac{1}{s})^{\frac{5}{2}})

Apply the chain rule:

\frac{5 ( s ^{6} + \frac{1}{s} ) ^{\frac{3}{2}}}{2} \frac{d}{d s} (s^{6} + \frac{1}{s})

= \frac{5 ( s ^{6} + \frac{1}{s} ) ^{\frac{3}{2}}}{2} \frac{d}{d s} (s^{6} + \frac{1}{s})

\frac{d}{d s} (s^{6} + \frac{1}{s}) = 6 s^{5} - \frac{1}{s ^{2}}

= \frac{5 ( s ^{6} + \frac{1}{s} ) ^{\frac{3}{2}}}{2} (6 s^{5} - \frac{1}{s ^{2}})

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (s^6+1/s)^{5/2} ?
The derivative of (s^6+1/s)^{5/2} is (5(s^6+1/s)^{3/2})/2 (6s^5-1/(s^2))
What is the first derivative of (s^6+1/s)^{5/2} ?
The first derivative of (s^6+1/s)^{5/2} is (5(s^6+1/s)^{3/2})/2 (6s^5-1/(s^2))