What is the derivative of ln(sqrt(b-ax)) ?

The derivative of ln(sqrt(b-ax)) is -a/(2(b-ax))

What is the first derivative of ln(sqrt(b-ax)) ?

The first derivative of ln(sqrt(b-ax)) is -a/(2(b-ax))

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\frac{d}{d x} (ln (b - a x))

- \frac{a}{2 ( b - a x )}

Solution steps

\frac{d}{d x} (ln (b - a x))

Apply the chain rule:

\frac{1}{b - a x} \frac{d}{d x} (b - a x)

= \frac{1}{b - a x} \frac{d}{d x} (b - a x)

\frac{d}{d x} (b - a x) = - \frac{a}{2 b - a x}

= \frac{1}{b - a x} (- \frac{a}{2 b - a x})

Simplify

\frac{1}{b - a x} (- \frac{a}{2 b - a x}) : - \frac{a}{2 ( b - a x )}

= - \frac{a}{2 ( b - a x )}

cos (x), x = \frac{π}{2}

y^{^{''}} - \frac{1}{t} y^{^{'}} + \frac{26}{t ^{2}} y = 0

\int 7 cos (x) d x

(\frac{1}{x} + x^{2} - 2)^{^{'}}

\frac{d}{d x} (19 + x)

What is the derivative of ln(sqrt(b-ax)) ?
The derivative of ln(sqrt(b-ax)) is -a/(2(b-ax))
What is the first derivative of ln(sqrt(b-ax)) ?
The first derivative of ln(sqrt(b-ax)) is -a/(2(b-ax))