(d^5)/(dx^5)(x^{11/2})

解答

\frac{d ^{5}}{d x ^{5}} (x^{\frac{11}{2}})

\frac{10395 x ^{\frac{1}{2}}}{32}

求解步骤

\frac{d ^{5}}{d x ^{5}} (x^{\frac{11}{2}})

\frac{d}{d x} (x^{\frac{11}{2}}) = \frac{11 x ^{\frac{9}{2}}}{2}

= \frac{d ^{4}}{d x ^{4}} (\frac{11 x ^{\frac{9}{2}}}{2})

\frac{d}{d x} (\frac{11 x ^{\frac{9}{2}}}{2}) = \frac{99 x ^{\frac{7}{2}}}{4}

= \frac{d ^{3}}{d x ^{3}} (\frac{99 x ^{\frac{7}{2}}}{4})

\frac{d}{d x} (\frac{99 x ^{\frac{7}{2}}}{4}) = \frac{693 x ^{\frac{5}{2}}}{8}

= \frac{d ^{2}}{d x ^{2}} (\frac{693 x ^{\frac{5}{2}}}{8})

\frac{d}{d x} (\frac{693 x ^{\frac{5}{2}}}{8}) = \frac{3465 x ^{\frac{3}{2}}}{16}

= \frac{d}{d x} (\frac{3465 x ^{\frac{3}{2}}}{16})

\frac{d}{d x} (\frac{3465 x ^{\frac{3}{2}}}{16}) = \frac{10395 x ^{\frac{1}{2}}}{32}

= \frac{10395 x ^{\frac{1}{2}}}{32}

\int x + 1 d x

x \to 0 lim (\frac{4}{x ^{3} ( x + 3 )})

t a y l or sin (x), 1

d er i v a t i v e \frac{x ^{2}}{28}

\frac{d}{d x} (cos (2 x) + sin (2 x))