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人気のある微分積分 >

derivative of {f}(xx)

解

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

解

x \frac{d}{d x} (f (x)) + f (x)

解答ステップ

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

積の法則を適用:

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

f = f (x), g = x

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

\frac{d x}{d x} = 1

= \frac{d}{d x} (f (x)) x + 1 \cdot f (x)

簡素化

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

人気の例

derivative of (2x+8x^2/((1+8x)^2))

\frac{d}{d x} (\frac{2 x + 8 x ^{2}}{( 1 + 8 x ) ^{2}})

sum from n=1 to infinity of (5n)/(4n+3)

n = 1 \sum \infty \frac{5 n}{4 n + 3}

limit as h approaches 3 of ((-3h+5-5))/h

h \to 3 lim (\frac{( - 3 h + 5 - 5 )}{h})

limit as x approaches 3+of ln(x-3)

x \to 3 + lim (ln (x - 3))

limit as x approaches-3 of x-3

x \to - 3 lim (x - 3)