What is (\partial)/(\partial x)(z(1+e^{x+y})) ?

The answer to (\partial)/(\partial x)(z(1+e^{x+y})) is e^{x+y}z

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(\partial)/(\partial x)(z(1+e^{x+y}))

\frac{\partial}{\partial x} (z (1 + e^{x + y}))

e^{x + y} z

Solution steps

\frac{\partial}{\partial x} (z (1 + e^{x + y}))

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (1) = 0

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

= z (0 + e^{x + y})

Simplify

= e^{x + y} z

\frac{d}{d x} (x^{a} y^{b})

(\frac{1}{x ^{2}} - \frac{5}{x ^{4}}) (x + 8 x^{3})

\int 7 x^{3} (x - 5)^{- 4} d x

\frac{d}{d x} (\frac{30}{( 1 - x ) ^{4}})

y^{^{'''}} + 4 y^{^{''}} - 6 y^{^{'}} - 12 y = 0

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