What is (\partial)/(\partial x)(ln(x)+zln(y)) ?

The answer to (\partial)/(\partial x)(ln(x)+zln(y)) is 1/x

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(\partial)/(\partial x)(ln(x)+zln(y))

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

\frac{1}{x}

Solution steps

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

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (ln (x)) = \frac{1}{x}

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

= \frac{1}{x} + 0

Simplify

= \frac{1}{x}

y^{^{''}} + 7 y^{^{'}} + 10 y = 3 e^{4 t}

\frac{d}{d x} (A x e^{x^{2}})

\int (2 sec^{2} (x) - x^{5}) d x

\int (x sin (y)) d y

x \to - 5 lim (\frac{8}{( x + 5 ) ^{6}})

What is (\partial)/(\partial x)(ln(x)+zln(y)) ?
The answer to (\partial)/(\partial x)(ln(x)+zln(y)) is 1/x