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

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

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

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

z (z + \frac{x}{y})

Solution steps

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

Treat

z, x

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (yz) = z

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

= z (z + \frac{x}{y})

e^{x} (x^{3} - \frac{486 x}{5}) + e^{x} (3 x^{2} - \frac{486}{5})

(z^{2} - 2 z + 1)^{8}

\frac{πj}{z ( z - π - πj ) ( z + π + πj )}

cos (x) \cdot (1 + \frac{tan ^{2} ( x )}{sec ( x ) + 1})

(2 - 4 x - 3) (2 + 4 x - 3)

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