derivative f(x)=1.5x^7-(x^4)/3+pix-ex^2+sqrt(2)

解

導関数

f (x) = 1.5 x^{7} - \frac{x ^{4}}{3} + π x - e x^{2} + 2

10.5 x^{6} - 1.33333 \dots x^{3} - 5.43656 \dots x + π

解答ステップ

\frac{d}{d x} (1.5 x^{7} - \frac{x ^{4}}{3} + π x - e x^{2} + 2)

簡素化

1.5 x^{7} - \frac{x ^{4}}{3} + π x - e x^{2} + 2 : 1.5 x^{7} - 0.33333 \dots x^{4} + π x - e x^{2} + 1.41421 \dots

= \frac{d}{d x} (1.5 x^{7} - 0.33333 \dots x^{4} + π x - e x^{2} + 1.41421 \dots)

和/差の法則を適用:

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

= \frac{d}{d x} (1.5 x^{7}) - \frac{d}{d x} (0.33333 \dots x^{4}) + \frac{d}{d x} (π x) - \frac{d}{d x} (e x^{2}) + \frac{d}{d x} (1.41421 \dots)

\frac{d}{d x} (1.5 x^{7}) = 10.5 x^{6}

\frac{d}{d x} (0.33333 \dots x^{4}) = 1.33333 \dots x^{3}

\frac{d}{d x} (π x) = π

\frac{d}{d x} (e x^{2}) = 2 e x

\frac{d}{d x} (1.41421 \dots) = 0

= 10.5 x^{6} - 1.33333 \dots x^{3} + π - 2 e x + 0

簡素化

= 10.5 x^{6} - 1.33333 \dots x^{3} - 5.43656 \dots x + π