derivative (x^7)/a+a/b x^6-cx

解答

导数

\frac{x ^{7}}{a} + \frac{a}{b} x^{6} - c x

\frac{7 x ^{6}}{a} + \frac{6 a x ^{5}}{b} - c

求解步骤

\frac{d}{d x} (\frac{x ^{7}}{a} + \frac{a}{b} x^{6} - c x)

化简

\frac{x ^{7}}{a} + \frac{a}{b} x^{6} - c x : \frac{x ^{7}}{a} + \frac{a x ^{6}}{b} - c x

= \frac{d}{d x} (\frac{x ^{7}}{a} + \frac{a x ^{6}}{b} - c x)

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{x ^{7}}{a}) + \frac{d}{d x} (\frac{a x ^{6}}{b}) - \frac{d}{d x} (c x)

\frac{d}{d x} (\frac{x ^{7}}{a}) = \frac{7 x ^{6}}{a}

\frac{d}{d x} (\frac{a x ^{6}}{b}) = \frac{6 a x ^{5}}{b}

\frac{d}{d x} (c x) = c

= \frac{7 x ^{6}}{a} + \frac{6 a x ^{5}}{b} - c

l a pl a ce t r an s f or m cos (t - 1)

\int \frac{1}{x ^{2} - 324} d x

\frac{d}{d x} ((x^{2} - 6) e^{8 x})

\int 0 x d x

d er i v a t i v e y = x^{2} (5 x - 1)^{3}