derivative h(x)=(x+1)^7-7x-3

解

導関数

h (x) = (x + 1)^{7} - 7 x - 3

7 x^{6} + 42 x^{5} + 105 x^{4} + 140 x^{3} + 105 x^{2} + 42 x

解答ステップ

\frac{d}{d x} ((x + 1)^{7} - 7 x - 3)

簡素化

(x + 1)^{7} - 7 x - 3 : x^{7} + 7 x^{6} + 21 x^{5} + 35 x^{4} + 35 x^{3} + 21 x^{2} - 2

= \frac{d}{d x} (x^{7} + 7 x^{6} + 21 x^{5} + 35 x^{4} + 35 x^{3} + 21 x^{2} - 2)

和/差の法則を適用:

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

= \frac{d}{d x} (x^{7}) + \frac{d}{d x} (7 x^{6}) + \frac{d}{d x} (21 x^{5}) + \frac{d}{d x} (35 x^{4}) + \frac{d}{d x} (35 x^{3}) + \frac{d}{d x} (21 x^{2}) - \frac{d}{d x} (2)

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

\frac{d}{d x} (7 x^{6}) = 42 x^{5}

\frac{d}{d x} (21 x^{5}) = 105 x^{4}

\frac{d}{d x} (35 x^{4}) = 140 x^{3}

\frac{d}{d x} (35 x^{3}) = 105 x^{2}

\frac{d}{d x} (21 x^{2}) = 42 x

\frac{d}{d x} (2) = 0

= 7 x^{6} + 42 x^{5} + 105 x^{4} + 140 x^{3} + 105 x^{2} + 42 x - 0

簡素化

= 7 x^{6} + 42 x^{5} + 105 x^{4} + 140 x^{3} + 105 x^{2} + 42 x