What is (\partial)/(\partial x)(x^2y+yln(xz^3)) ?

The answer to (\partial)/(\partial x)(x^2y+yln(xz^3)) is 2yx+y/x

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(\partial)/(\partial x)(x^2y+yln(xz^3))

\frac{\partial}{\partial x} (x^{2} y + y ln (x z^{3}))

2 y x + \frac{y}{x}

Solution steps

\frac{\partial}{\partial x} (x^{2} y + y ln (x z^{3}))

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= 2 y x + \frac{y}{x}

\int 3 x^{4} + \frac{7}{4} x^{5} d x

y^{^{'}} + y + 4 cos (x) = 0

\frac{d}{d x} (\frac{( x + 1 )}{( x - 1 )})

y = 2 ln (3) + \frac{1}{2} ln (x^{2} + 1)

\frac{d}{d x} (2 x (4 - x^{2})^{\frac{1}{2}})

What is (\partial)/(\partial x)(x^2y+yln(xz^3)) ?
The answer to (\partial)/(\partial x)(x^2y+yln(xz^3)) is 2yx+y/x