What is (\partial)/(\partial x)(yln(5x+y)) ?

The answer to (\partial)/(\partial x)(yln(5x+y)) is (5y)/(5x+y)

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(\partial)/(\partial x)(yln(5x+y))

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

\frac{5 y}{5 x + y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{5 x + y} \frac{\partial}{\partial x} (5 x + y)

= \frac{1}{5 x + y} \frac{\partial}{\partial x} (5 x + y)

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

= y \frac{1}{5 x + y} \cdot 5

Simplify

y \frac{1}{5 x + y} \cdot 5 : \frac{5 y}{5 x + y}

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

\int_{1}^{6} 7 \frac{ln ( x )}{x ^{2}} d x

\int sin (2 x) e^{c o s^{2} (x)} d x

x \to 3 lim (\frac{6}{x - 3})

2 x - 3

x \to - 1 - lim (\frac{1}{x + 1})

What is (\partial)/(\partial x)(yln(5x+y)) ?
The answer to (\partial)/(\partial x)(yln(5x+y)) is (5y)/(5x+y)