derivative 6x^5(x-4)^5+5(x-4)^4x^6

פתרון

derivative of

6 x^{5} (x - 4)^{5} + 5 (x - 4)^{4} x^{6}

110 x^{9} - 1800 x^{8} + 11520 x^{7} - 35840 x^{6} + 53760 x^{5} - 30720 x^{4}

צעדי פתרון

\frac{d}{d x} (6 x^{5} (x - 4)^{5} + 5 (x - 4)^{4} x^{6})

6 x^{5} (x - 4)^{5} + 5 (x - 4)^{4} x^{6}

פשט את:

11 x^{10} - 200 x^{9} + 1440 x^{8} - 5120 x^{7} + 8960 x^{6} - 6144 x^{5}

= \frac{d}{d x} (11 x^{10} - 200 x^{9} + 1440 x^{8} - 5120 x^{7} + 8960 x^{6} - 6144 x^{5})

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

:השתמש בחוק החיבור

= \frac{d}{d x} (11 x^{10}) - \frac{d}{d x} (200 x^{9}) + \frac{d}{d x} (1440 x^{8}) - \frac{d}{d x} (5120 x^{7}) + \frac{d}{d x} (8960 x^{6}) - \frac{d}{d x} (6144 x^{5})

\frac{d}{d x} (11 x^{10}) = 110 x^{9}

\frac{d}{d x} (200 x^{9}) = 1800 x^{8}

\frac{d}{d x} (1440 x^{8}) = 11520 x^{7}

\frac{d}{d x} (5120 x^{7}) = 35840 x^{6}

\frac{d}{d x} (8960 x^{6}) = 53760 x^{5}

\frac{d}{d x} (6144 x^{5}) = 30720 x^{4}

= 110 x^{9} - 1800 x^{8} + 11520 x^{7} - 35840 x^{6} + 53760 x^{5} - 30720 x^{4}

\frac{\partial}{\partial x} (\frac{- c x}{x ^{2} + y ^{2}})

in v erse l a pl a ce \frac{k ^{4}}{( s + k ) ^{5}}

\frac{\partial}{\partial x} (\frac{( y ^{4} )}{x})

2 y^{^{'}} - y = 0

x \to 0 lim (5 x - 12)