What is the derivative of ln(5x+ln(3x)) ?

The derivative of ln(5x+ln(3x)) is (5x+1)/(x(5x+ln(3x)))

What is the first derivative of ln(5x+ln(3x)) ?

The first derivative of ln(5x+ln(3x)) is (5x+1)/(x(5x+ln(3x)))

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derivative of

ln (5 x + ln (3 x))

\frac{5 x + 1}{x ( 5 x + ln ( 3 x ) )}

Solution steps

\frac{d}{d x} (ln (5 x + ln (3 x)))

Apply the chain rule:

\frac{1}{5 x + ln ( 3 x )} \frac{d}{d x} (5 x + ln (3 x))

= \frac{1}{5 x + ln ( 3 x )} \frac{d}{d x} (5 x + ln (3 x))

\frac{d}{d x} (5 x + ln (3 x)) = 5 + \frac{1}{x}

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

Simplify

\frac{1}{5 x + ln ( 3 x )} (5 + \frac{1}{x}) : \frac{5 x + 1}{x ( 5 x + ln ( 3 x ) )}

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

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

\frac{d}{d x} (1700 e^{x})

\int (6 x^{2} y - 3 x y) d y

\int 3 sin (2 θ) d θ

3 x^{4} + 9 x^{3} + 11

What is the derivative of ln(5x+ln(3x)) ?
The derivative of ln(5x+ln(3x)) is (5x+1)/(x(5x+ln(3x)))
What is the first derivative of ln(5x+ln(3x)) ?
The first derivative of ln(5x+ln(3x)) is (5x+1)/(x(5x+ln(3x)))