What is the derivative of arcsin(ln(kx+9)) ?

The derivative of arcsin(ln(kx+9)) is k/((kx+9)sqrt(1-ln^2(kx+9)))

What is the first derivative of arcsin(ln(kx+9)) ?

The first derivative of arcsin(ln(kx+9)) is k/((kx+9)sqrt(1-ln^2(kx+9)))

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\frac{d}{d x} (arcsin (ln (k x + 9)))

\frac{k}{( k x + 9 ) 1 - ln ^{2} ( k x + 9 )}

Solution steps

\frac{d}{d x} (arcsin (ln (k x + 9)))

Apply the chain rule:

\frac{1}{1 - ( ln ( k x + 9 ) ) ^{2}} \frac{d}{d x} (ln (k x + 9))

= \frac{1}{1 - ( ln ( k x + 9 ) ) ^{2}} \frac{d}{d x} (ln (k x + 9))

\frac{d}{d x} (ln (k x + 9)) = \frac{k}{k x + 9}

= \frac{1}{1 - ( ln ( k x + 9 ) ) ^{2}} \cdot \frac{k}{k x + 9}

Simplify

\frac{1}{1 - ln ^{2} ( k x + 9 )} \cdot \frac{k}{k x + 9} : \frac{k}{( k x + 9 ) 1 - ln ^{2} ( k x + 9 )}

= \frac{k}{( k x + 9 ) 1 - ln ^{2} ( k x + 9 )}

\int 2 e^{- t} t d t

\int e^{- 10 r^{2}} d r

(x - 1) \cdot ln (x - 1), 2

9 - x^{2}, 0

\int \frac{7 x ^{4} - 6 x ^{2} - x + 5}{x + 2} d x

What is the derivative of arcsin(ln(kx+9)) ?
The derivative of arcsin(ln(kx+9)) is k/((kx+9)sqrt(1-ln^2(kx+9)))
What is the first derivative of arcsin(ln(kx+9)) ?
The first derivative of arcsin(ln(kx+9)) is k/((kx+9)sqrt(1-ln^2(kx+9)))