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Popular >

derivative of ln(x+sqrt(1-x^2))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

sum from n=0 to infinity of (5/4)(2/3)^n

n = 0 \sum \infty (\frac{5}{4}) (\frac{2}{3})^{n}

sum from n=0 to infinity of n/(n^2+2)

n = 0 \sum \infty \frac{n}{n ^{2} + 2}

integral of ((x^2)/2-2/(x^2))

\int (\frac{x ^{2}}{2} - \frac{2}{x ^{2}}) d x

(\partial)/(\partial x)((3y)/(x^2+2))

\frac{\partial}{\partial x} (\frac{3 y}{x ^{2} + 2})

derivative of 3/4 x^{4/3}-3/8 x^{2/3}

\frac{d}{d x} (\frac{3}{4} x^{\frac{4}{3}} - \frac{3}{8} x^{\frac{2}{3}})

Frequently Asked Questions (FAQ)

What is the derivative of ln(x+sqrt(1-x^2)) ?
The derivative of ln(x+sqrt(1-x^2)) is (sqrt(1-x^2)-x)/((x+sqrt(1-x^2))\sqrt{1-x^2)}
What is the first derivative of ln(x+sqrt(1-x^2)) ?
The first derivative of ln(x+sqrt(1-x^2)) is (sqrt(1-x^2)-x)/((x+sqrt(1-x^2))\sqrt{1-x^2)}