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人気のある微分積分 >

derivative x^9sin(x)

解

導関数

x^{9} sin (x)

解

9 x^{8} sin (x) + cos (x) x^{9}

解答ステップ

\frac{d}{d x} (x^{9} sin (x))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{9}, g = sin (x)

= \frac{d}{d x} (x^{9}) sin (x) + \frac{d}{d x} (sin (x)) x^{9}

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

\frac{d}{d x} (sin (x)) = cos (x)

= 9 x^{8} sin (x) + cos (x) x^{9}

グラフ

人気の例

derivative (x-5)(5x+3)

d er i v a t i v e (x - 5) (5 x + 3)

derivative x^{-4}

d er i v a t i v e x^{- 4}

integral from 2 to 4 of 6/(2x-9)

\int_{2}^{4} \frac{6}{2 x - 9} d x

limit as x approaches 8 of x+2

x \to 8 lim (x + 2)

tangent f(x)=ln(x^3-7),\at x=2

t an g e n t f (x) = ln (x^{3} - 7), at x = 2