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人気のある微分積分 >

derivative of x^9{f}(x)

解

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

解

9 x^{8} f (x) + \frac{d}{d x} (f (x)) x^{9}

解答ステップ

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

積の法則を適用:

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

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

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

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

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

人気の例

derivative of ce^{x/6}

\frac{d}{d x} (c e^{\frac{x}{6}})

integral of 4x^2-sin(x)+C

\int 4 x^{2} - sin (x) + C d x

integral of 1/(x^3)+x

\int \frac{1}{x ^{3}} + x d x

derivative (x-3)/2

d er i v a t i v e \frac{x - 3}{2}

(\partial)/(\partial x)(x^3yz^2+7yz)

\frac{\partial}{\partial x} (x^{3} y z^{2} + 7 yz)