What is (\partial)/(\partial x)(xe^y-e^z) ?

The answer to (\partial)/(\partial x)(xe^y-e^z) is e^y

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(\partial)/(\partial x)(xe^y-e^z)

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

e^{y}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (e^{z}) = 0

= e^{y} - 0

Simplify

= e^{y}

\frac{d y}{d x}, y e^{x} = y

\frac{d}{d x} ((3 x + 1) \frac{( x ^{2} + 4 )}{( 6 x - 5 )})

\int \frac{sin ( 2 x )}{sin ( x )} d x

y = 2 csc (8 x^{3} - 8 x + 8)

\int_{0}^{1} 8 cos (4 x) d x

What is (\partial)/(\partial x)(xe^y-e^z) ?
The answer to (\partial)/(\partial x)(xe^y-e^z) is e^y