What is the d/(ds)(sqrt(s^2+t^2)) ?

The d/(ds)(sqrt(s^2+t^2)) is s/(sqrt(s^2+t^2))

What is the first d/(ds)(sqrt(s^2+t^2)) ?

The first d/(ds)(sqrt(s^2+t^2)) is s/(sqrt(s^2+t^2))

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\frac{d}{d s} (s^{2} + t^{2})

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

Solution steps

\frac{d}{d s} (s^{2} + t^{2})

Treat

t

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the d/(ds)(sqrt(s^2+t^2)) ?
The d/(ds)(sqrt(s^2+t^2)) is s/(sqrt(s^2+t^2))
What is the first d/(ds)(sqrt(s^2+t^2)) ?
The first d/(ds)(sqrt(s^2+t^2)) is s/(sqrt(s^2+t^2))