d/(dt)(sqrt(5t)+(sqrt(7))/t)

解答

\frac{d}{d t} (5 t + \frac{7}{t})

\frac{5 t ^{\frac{3}{2}} - 2 7}{2 t ^{\frac{3}{2}} t}

求解步骤

\frac{d}{d t} (5 t + \frac{7}{t})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (5 t) + \frac{d}{d t} (\frac{7}{t})

\frac{d}{d t} (5 t) = \frac{5}{2 t}

\frac{d}{d t} (\frac{7}{t}) = - \frac{7}{t ^{2}}

= \frac{5}{2 t} - \frac{7}{t ^{2}}

化简

\frac{5}{2 t} - \frac{7}{t ^{2}} : \frac{5 t ^{\frac{3}{2}} - 2 7}{2 t ^{\frac{3}{2}} t}

= \frac{5 t ^{\frac{3}{2}} - 2 7}{2 t ^{\frac{3}{2}} t}

\int cos^{3} (t) - sin^{2} (t) cos (t) d t

d er i v a t i v e y = x^{2} - 5 x - 6

d er i v a t i v e f (x) = \frac{( x + 9 )}{x ^{2} - 7 x + 1}

d er i v a t i v e g (x) = \frac{7}{x}

\int \frac{4 x ^{5}}{1 - 12 x ^{6}} d x