What is (d^3)/(dx^3)(sqrt(1+x^2)) ?

The answer to (d^3)/(dx^3)(sqrt(1+x^2)) is -(3x)/((1+x^2)^{5/2)}

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(d^3)/(dx^3)(sqrt(1+x^2))

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

- \frac{3 x}{( 1 + x ^{2} ) ^{\frac{5}{2}}}

Solution steps

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

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

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

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

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

\frac{d}{d x} (\frac{1}{( 1 + x ^{2} ) 1 + x ^{2}}) = - \frac{3 x}{( 1 + x ^{2} ) ^{\frac{5}{2}}}

= - \frac{3 x}{( 1 + x ^{2} ) ^{\frac{5}{2}}}

\int 5 x + sin (x) d x

x \to - 4 lim (x + 4)

(y + 4) (\frac{d y}{d x}) = 2 x y + 4 y

\frac{d y}{d x} = 4 x e^{2 y}

\frac{1}{c}

What is (d^3)/(dx^3)(sqrt(1+x^2)) ?
The answer to (d^3)/(dx^3)(sqrt(1+x^2)) is -(3x)/((1+x^2)^{5/2)}