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Popular >

derivative of arcsin(xln(x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral from 0 to 1 of 5/(1+x^2)

\int_{0}^{1} \frac{5}{1 + x ^{2}} d x

(1+y/(x^2))dx-1/x dy=0

(1 + \frac{y}{x ^{2}}) d x - \frac{1}{x} d y = 0

(\partial)/(\partial x)((x^2)/(2y))

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

derivative of-1/(4sin(x))

\frac{d}{d x} (- \frac{1}{4 sin ( x )})

1/(-0.75y-0.00003)y^'=1

\frac{1}{- 0.75 y - 0.00003} y^{^{'}} = 1

Frequently Asked Questions (FAQ)

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