What is (\partial)/(\partial t)(-(sqrt(s^2+t^2))) ?

The answer to (\partial)/(\partial t)(-(sqrt(s^2+t^2))) is -t/(sqrt(s^2+t^2))

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(\partial)/(\partial t)(-(sqrt(s^2+t^2)))

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

- \frac{t}{s ^{2} + t ^{2}}

Solution steps

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

Treat

s

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{2 s ^{2} + t ^{2}} \cdot 2 t : - \frac{t}{s ^{2} + t ^{2}}

= - \frac{t}{s ^{2} + t ^{2}}

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What is (\partial)/(\partial t)(-(sqrt(s^2+t^2))) ?
The answer to (\partial)/(\partial t)(-(sqrt(s^2+t^2))) is -t/(sqrt(s^2+t^2))