What is (\partial)/(\partial x)((z)(yz+xln(y))) ?

The answer to (\partial)/(\partial x)((z)(yz+xln(y))) is zln(y)

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(\partial)/(\partial x)((z)(yz+xln(y)))

\frac{\partial}{\partial x} ((z) (yz + x ln (y)))

z ln (y)

Solution steps

\frac{\partial}{\partial x} ((z) (yz + x ln (y)))

Treat

z, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= z \frac{\partial}{\partial x} (yz + x ln (y))

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (yz) + \frac{\partial}{\partial x} (x ln (y)))

\frac{\partial}{\partial x} (yz) = 0

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

= z (0 + ln (y))

Simplify

= z ln (y)

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

7^{2}

(sin (x) + csc (x))^{2} + (cos (x) + sec (x))^{2}

ln (9)

2 lo g_{4} (8) x^{3} y

What is (\partial)/(\partial x)((z)(yz+xln(y))) ?
The answer to (\partial)/(\partial x)((z)(yz+xln(y))) is zln(y)