What is (\partial)/(\partial y)(2xln(y)-yz) ?

The answer to (\partial)/(\partial y)(2xln(y)-yz) is (2x)/y-z

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(\partial)/(\partial y)(2xln(y)-yz)

\frac{\partial}{\partial y} (2 x ln (y) - yz)

\frac{2 x}{y} - z

Solution steps

\frac{\partial}{\partial y} (2 x ln (y) - yz)

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (2 x ln (y)) - \frac{\partial}{\partial y} (yz)

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

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

= \frac{2 x}{y} - z

(e^{- x} - e^{5}) (e^{x} + e^{- 2})

y^{^{''}} - 2 y + y = t + 1, y (0) = 0, y^{^{'}} (0) = 0

f (x) = - \frac{2}{x}

\frac{\partial}{\partial x} (4 x e^{4 x y})

What is (\partial)/(\partial y)(2xln(y)-yz) ?
The answer to (\partial)/(\partial y)(2xln(y)-yz) is (2x)/y-z