What is (\partial)/(\partial s)(sqrt(s^6+t^6)) ?

The answer to (\partial)/(\partial s)(sqrt(s^6+t^6)) is (3s^5)/(sqrt(s^6+t^6))

(\partial)/(\partial s)(sqrt(s^6+t^6))

\frac{\partial}{\partial s} (s^{6} + t^{6})

\frac{3 s ^{5}}{s ^{6} + t ^{6}}

Solution steps

\frac{\partial}{\partial s} (s^{6} + t^{6})

Treat

t

as a constant

Apply the chain rule:

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

= \frac{1}{2 s ^{6} + t ^{6}} \frac{\partial}{\partial s} (s^{6} + t^{6})

\frac{\partial}{\partial s} (s^{6} + t^{6}) = 6 s^{5}

= \frac{1}{2 s ^{6} + t ^{6}} \cdot 6 s^{5}

Simplify

\frac{1}{2 s ^{6} + t ^{6}} \cdot 6 s^{5} : \frac{3 s ^{5}}{s ^{6} + t ^{6}}

= \frac{3 s ^{5}}{s ^{6} + t ^{6}}

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What is (\partial)/(\partial s)(sqrt(s^6+t^6)) ?
The answer to (\partial)/(\partial s)(sqrt(s^6+t^6)) is (3s^5)/(sqrt(s^6+t^6))