What is the derivative of arcsin(ln(x)) ?

The derivative of arcsin(ln(x)) is 1/(xsqrt(1-ln^2(x)))

What is the first derivative of arcsin(ln(x)) ?

The first derivative of arcsin(ln(x)) is 1/(xsqrt(1-ln^2(x)))

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derivative of

arcsin (ln (x))

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

Solution steps

\frac{d}{d x} (arcsin (ln (x)))

Apply the chain rule:

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

Simplify

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

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

f (x) = 5 + 4 x - x^{3}

n = 0 \sum \infty (- 1)^{n} (n^{3})

\frac{\partial}{\partial x} (x^{8} y^{8} - x^{7} y^{7})

\frac{\partial}{\partial x} (sinh (x))

\int 10 cos (3 x) d x

What is the derivative of arcsin(ln(x)) ?
The derivative of arcsin(ln(x)) is 1/(xsqrt(1-ln^2(x)))
What is the first derivative of arcsin(ln(x)) ?
The first derivative of arcsin(ln(x)) is 1/(xsqrt(1-ln^2(x)))