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

The answer to (\partial)/(\partial s)((x)(s^2+t^2)) is 2xs

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(\partial)/(\partial s)((x)(s^2+t^2))

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

2 x s

Solution steps

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

Treat

x, t

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial s} (t^{2}) = 0

= x (2 s + 0)

Simplify

= 2 x s

(x cos (θ) + y sin (θ))^{2}

2 (u^{2} + v^{2}) 2 u^{2} + 2 v^{2} + 4

\frac{42 e ^{x} ( - 7 e ^{x} + 6 )}{( 7 e ^{x} + 6 ) ^{3}}

\frac{8}{( x + 4 ) ^{2}}

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