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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

xy^2y^'=x^3+y^3

x y^{2} y^{^{'}} = x^{3} + y^{3}

integral from 0 to pi/6 of ln(sec(x))

\int_{0}^{\frac{π}{6}} ln (sec (x)) d x

area y=sqrt(x),y=x^2,x=2 area

y = x, y = x^{2}, x = 2

laplacetransform f(t)=t^3 laplace transform

f (t) = t^{3}

derivative of (qx+r)/(sx+t)derivative of

\frac{q x + r}{s x + t}

Frequently Asked Questions (FAQ)

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