What is (d^4)/(dx^4)(arctan(x)) ?

The answer to (d^4)/(dx^4)(arctan(x)) is (24x(-x^2+1))/((x^2+1)^4)

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(d^4)/(dx^4)(arctan(x))

\frac{d ^{4}}{d x ^{4}} (arctan (x))

\frac{24 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{4}}

Solution steps

\frac{d ^{4}}{d x ^{4}} (arctan (x))

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

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

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

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

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

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

\frac{d}{d x} (- \frac{2 ( - 3 x ^{2} + 1 )}{( x ^{2} + 1 ) ^{3}}) = \frac{24 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{4}}

= \frac{24 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{4}}

\int (x^{3} - 10 x - 3) d x

\int_{2}^{4} (\frac{6 + x ^{2}}{x ^{3}}) d x

x \to 0 + lim (ln (x^{2}))

\frac{d}{d x} (a x^{2} + b y (x)^{2})

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

What is (d^4)/(dx^4)(arctan(x)) ?
The answer to (d^4)/(dx^4)(arctan(x)) is (24x(-x^2+1))/((x^2+1)^4)