What is (\partial)/(\partial x)(x+y/z) ?

The answer to (\partial)/(\partial x)(x+y/z) is 1

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(\partial)/(\partial x)(x+y/z)

\frac{\partial}{\partial x} (x + \frac{y}{z})

1

Solution steps

\frac{\partial}{\partial x} (x + \frac{y}{z})

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (\frac{y}{z})

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

\frac{\partial}{\partial x} (\frac{y}{z}) = 0

= 1 + 0

Simplify

= 1

y^{^{''}} - 8 y^{^{'}} + 17 y = 0

3 x^{2} y^{^{'}} = y^{^{'}} + 5 x e^{- y}

3 x^{2}, \frac{1}{3} x

\frac{d y}{d x} = (1 + e^{x}) y

\int cos^{2} (5 x) d x

What is (\partial)/(\partial x)(x+y/z) ?
The answer to (\partial)/(\partial x)(x+y/z) is 1