What is (\partial)/(\partial x)(ln(sqrt(3x)+5y)) ?

The answer to (\partial)/(\partial x)(ln(sqrt(3x)+5y)) is (sqrt(3))/(2sqrt(x)(\sqrt{3)sqrt(x)+5y)}

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(\partial)/(\partial x)(ln(sqrt(3x)+5y))

\frac{\partial}{\partial x} (ln (3 x + 5 y))

\frac{3}{2 x ( 3 x + 5 y )}

Solution steps

\frac{\partial}{\partial x} (ln (3 x + 5 y))

Simplify

ln (3 x + 5 y) : ln (3 x + 5 y)

= \frac{\partial}{\partial x} (ln (3 x + 5 y))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{3 x + 5 y} \frac{\partial}{\partial x} (3 x + 5 y)

= \frac{1}{3 x + 5 y} \frac{\partial}{\partial x} (3 x + 5 y)

\frac{\partial}{\partial x} (3 x + 5 y) = \frac{3}{2 x}

= \frac{1}{3 x + 5 y} \cdot \frac{3}{2 x}

Simplify

\frac{1}{3 x + 5 y} \cdot \frac{3}{2 x} : \frac{3}{2 x ( 3 x + 5 y )}

= \frac{3}{2 x ( 3 x + 5 y )}

x \to π lim ((2 x - 2 π) cot (x))

\frac{d}{d x} (cos (x^{2} - 1))

\frac{\partial}{\partial x} (\frac{6 x}{x ^{2} + y ^{2}})

y^{^{'}} = 2 x + y, y (0) = 7

sin (x) (cos (x) - 1) π

What is (\partial)/(\partial x)(ln(sqrt(3x)+5y)) ?
The answer to (\partial)/(\partial x)(ln(sqrt(3x)+5y)) is (sqrt(3))/(2sqrt(x)(\sqrt{3)sqrt(x)+5y)}