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Popular >

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

Solution

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

Solution

\frac{3 x ^{2} + 2}{x ( x ^{2} + 1 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{2} x^{2} + 1) = \frac{3 x ^{3} + 2 x}{x ^{2} + 1}

= \frac{1}{x ^{2} x ^{2} + 1} \cdot \frac{3 x ^{3} + 2 x}{x ^{2} + 1}

Simplify

\frac{1}{x ^{2} x ^{2} + 1} \cdot \frac{3 x ^{3} + 2 x}{x ^{2} + 1} : \frac{3 x ^{2} + 2}{x ( x ^{2} + 1 )}

= \frac{3 x ^{2} + 2}{x ( x ^{2} + 1 )}

Popular Examples

(dy}{dx}=\frac{(6xsec(y/x)+y))/x

\frac{d y}{d x} = \frac{( 6 x sec ( \frac{y}{x} ) + y )}{x}

taylor cos(x)+1/x , pi/2 taylor

cos (x) + \frac{1}{x}, \frac{π}{2}

tangent of f(x)=sqrt(x^2+18x+86),\at x=0 tangent of

f (x) = x^{2} + 18 x + 86, at x = 0

integral of-1/2 e^{-2x}

\int - \frac{1}{2} e^{- 2 x} d x

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

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

Frequently Asked Questions (FAQ)

What is the derivative of ln(x^2sqrt(x^2+1)) ?
The derivative of ln(x^2sqrt(x^2+1)) is (3x^2+2)/(x(x^2+1))
What is the first derivative of ln(x^2sqrt(x^2+1)) ?
The first derivative of ln(x^2sqrt(x^2+1)) is (3x^2+2)/(x(x^2+1))