What is (\partial)/(\partial x)(4+ln(xy-5)) ?

The answer to (\partial)/(\partial x)(4+ln(xy-5)) is y/(xy-5)

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(\partial)/(\partial x)(4+ln(xy-5))

\frac{\partial}{\partial x} (4 + ln (x y - 5))

\frac{y}{x y - 5}

Solution steps

\frac{\partial}{\partial x} (4 + ln (x y - 5))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4) + \frac{\partial}{\partial x} (ln (x y - 5))

\frac{\partial}{\partial x} (4) = 0

\frac{\partial}{\partial x} (ln (x y - 5)) = \frac{y}{y x - 5}

= 0 + \frac{y}{y x - 5}

Simplify

= \frac{y}{x y - 5}

\int 4^{k} d k

f (θ) = \frac{sin ( θ )}{1 + cos ( θ )}

\frac{d}{d x} (2 x^{3} + 15 x^{2} - 84 x + 10)

30 e^{x^{2}} x

x \to 0 + lim (x n (x))

What is (\partial)/(\partial x)(4+ln(xy-5)) ?
The answer to (\partial)/(\partial x)(4+ln(xy-5)) is y/(xy-5)