What is (\partial)/(\partial x)(e^{xz}y^3-ln(x)) ?

The answer to (\partial)/(\partial x)(e^{xz}y^3-ln(x)) is y^3e^{xz}z-1/x

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(\partial)/(\partial x)(e^{xz}y^3-ln(x))

\frac{\partial}{\partial x} (e^{x z} y^{3} - ln (x))

y^{3} e^{x z} z - \frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (e^{x z} y^{3} - ln (x))

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (e^{x z} y^{3}) - \frac{\partial}{\partial x} (ln (x))

\frac{\partial}{\partial x} (e^{x z} y^{3}) = y^{3} e^{x z} z

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

= y^{3} e^{x z} z - \frac{1}{x}

\frac{d}{d x} (arctan (11 x))

e^{4 z} - 4 e^{- 4 z}

\frac{\partial}{\partial y} (sin (x) sin (y))

(x + y) d x - (x - y) d y = 0, y (1) = 0

\int \frac{s}{s ^{2} + 6 s + 11} d s

What is (\partial)/(\partial x)(e^{xz}y^3-ln(x)) ?
The answer to (\partial)/(\partial x)(e^{xz}y^3-ln(x)) is y^3e^{xz}z-1/x