What is the derivative of f(x)=ln(sqrt(5x-7)) ?

The derivative of f(x)=ln(sqrt(5x-7)) is 5/(2(5x-7))

What is the first derivative of f(x)=ln(sqrt(5x-7)) ?

The first derivative of f(x)=ln(sqrt(5x-7)) is 5/(2(5x-7))

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derivative of

f (x) = ln (5 x - 7)

\frac{5}{2 ( 5 x - 7 )}

Solution steps

\frac{d}{d x} (ln (5 x - 7))

Apply the chain rule:

\frac{1}{5 x - 7} \frac{d}{d x} (5 x - 7)

= \frac{1}{5 x - 7} \frac{d}{d x} (5 x - 7)

\frac{d}{d x} (5 x - 7) = \frac{5}{2 5 x - 7}

= \frac{1}{5 x - 7} \cdot \frac{5}{2 5 x - 7}

Simplify

\frac{1}{5 x - 7} \cdot \frac{5}{2 5 x - 7} : \frac{5}{2 ( 5 x - 7 )}

= \frac{5}{2 ( 5 x - 7 )}

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What is the derivative of f(x)=ln(sqrt(5x-7)) ?
The derivative of f(x)=ln(sqrt(5x-7)) is 5/(2(5x-7))
What is the first derivative of f(x)=ln(sqrt(5x-7)) ?
The first derivative of f(x)=ln(sqrt(5x-7)) is 5/(2(5x-7))