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

The answer to (\partial)/(\partial y)(e^{xz}y^3-ln(x)) is 3e^{xz}y^2

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

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

3 e^{x z} y^{2}

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (e^{x z} y^{3}) = 3 e^{x z} y^{2}

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

= 3 e^{x z} y^{2} - 0

Simplify

= 3 e^{x z} y^{2}

\frac{d}{d x} (f (x) (x^{3}))

\int x (x + 3)^{7} d x

x^{2} \frac{d y}{d x} = y (4 x + 3)

\int_{- 1}^{1} \frac{1}{x ^{2}} d x

\frac{\partial}{\partial y} (6 z e^{x yz})

What is (\partial)/(\partial y)(e^{xz}y^3-ln(x)) ?
The answer to (\partial)/(\partial y)(e^{xz}y^3-ln(x)) is 3e^{xz}y^2