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}}

3 x^{4} - 7 x^{2}, at x = - 1

\int \frac{- 2 x + 4}{( x ^{2} + 1 ) ( x - 1 ) ^{2}} d x

\frac{d y}{d x} = 4 y^{2} sec^{2} (2 x), y (\frac{π}{8}) = 1

x \to - 3 lim (\frac{1}{2} - x^{3})

\int - tan (3 x) d x

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))