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Popular >

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

Solution

derivative of

ln (x + 1 + x^{2})

Solution

\frac{1}{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}{1 + x ^{2}}

= \frac{1}{1 + x ^{2}}

Popular Examples

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

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

limit as x approaches infinity of (256^{x/2})/(4^{2x)}

x \to \infty lim (\frac{25 6 ^{\frac{x}{2}}}{4 ^{2 x}})

integral of 6/(x^2+4)

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

limit as x approaches 1 of (x^2+1)/(x-1)

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

limit as x approaches 3 of 2ln(x-4)

x \to 3 lim (2 ln (x - 4))

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 1/(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 1/(sqrt(1+x^2))