What is (\partial)/(\partial r)((x)(r+s)) ?

The answer to (\partial)/(\partial r)((x)(r+s)) is x

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(\partial)/(\partial r)((x)(r+s))

\frac{\partial}{\partial r} ((x) (r + s))

x

Solution steps

\frac{\partial}{\partial r} ((x) (r + s))

Treat

x, s

as constants

Take the constant out:

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

= x \frac{\partial}{\partial r} (r + s)

Apply the Sum/Difference Rule:

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

= x (\frac{\partial}{\partial r} (r) + \frac{\partial}{\partial r} (s))

\frac{\partial}{\partial r} (r) = 1

\frac{\partial}{\partial r} (s) = 0

= x (1 + 0)

Simplify

= x

\frac{5 x + 2}{( x + 2 ) ( x + 1 )}

x (x y^{2} + x^{2} = x + 3 y)

\frac{2 y ^{2} - 2 x ^{2}}{( x ^{2} + y ^{2} ) ^{2}}

\frac{4 - e ^{- t}}{( e ^{- t} + 1 ) ( e ^{- t} + 2 )}

\frac{\partial}{\partial y} ((x) (y^{4} + 3 y - 4 x^{3} - 5 x))

What is (\partial)/(\partial r)((x)(r+s)) ?
The answer to (\partial)/(\partial r)((x)(r+s)) is x