derivative of arctan(((a^2-x^3)/(b^2)))

Lösung

\frac{d}{d x} (arctan (\frac{( a ^{2} - x ^{3} )}{b ^{2}}))

- \frac{3 b ^{2} x ^{2}}{( - x ^{3} + a ^{2} ) ^{2} + b ^{4}}

Schritte zur Lösung

\frac{d}{d x} (arctan (\frac{( a ^{2} - x ^{3} )}{b ^{2}}))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{a ^{2} - x ^{3}}{b ^{2}}) = - \frac{3 x ^{2}}{b ^{2}}

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

Vereinfache

\frac{1}{( \frac{a ^{2} - x ^{3}}{b ^{2}} ) ^{2} + 1} (- \frac{3 x ^{2}}{b ^{2}}) : - \frac{3 b ^{2} x ^{2}}{( - x ^{3} + a ^{2} ) ^{2} + b ^{4}}

= - \frac{3 b ^{2} x ^{2}}{( - x ^{3} + a ^{2} ) ^{2} + b ^{4}}

\frac{d}{d x} (\frac{1 - 2 x ^{2}}{x ^{4} - 2 x ^{2} + 6})

\int 1 + (4 x)^{2} d x

\int \frac{1}{sin ( x ) cos ^{2} ( x )} d x

t an g e n t f (x) = 10 sin (x) + 103 cos (x)

in v erse l a pl a ce \frac{2}{s ^{2} + 3 s + 2}