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

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

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

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

e^{x z} x y^{3}

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= y^{3} e^{x z} x - 0

Simplify

= e^{x z} x y^{3}

(x - 1)^{3}, x - 1, 0, 2

f (x) = \frac{2}{2 x + 1}

(x + y)^{2} d x + (2 x y + x^{2} - 5) d y = 0

\frac{\partial}{\partial y} (\frac{1}{x ^{2} + y ^{2}})

x \to 0 lim (\frac{1}{x} + \frac{1}{x ^{2} - x})

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