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人気のある微分積分 >

derivative of xsqrt(x-3)

解

\frac{d}{d x} (x x - 3)

解

\frac{3 x - 6}{2 x - 3}

解答ステップ

\frac{d}{d x} (x x - 3)

積の法則を適用:

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

f = x, g = x - 3

= \frac{d x}{d x} x - 3 + \frac{d}{d x} (x - 3) x

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

\frac{d}{d x} (x - 3) = \frac{1}{2 x - 3}

= 1 \cdot x - 3 + \frac{1}{2 x - 3} x

簡素化

1 \cdot x - 3 + \frac{1}{2 x - 3} x : \frac{3 x - 6}{2 x - 3}

= \frac{3 x - 6}{2 x - 3}

グラフ

人気の例

integral of 3sin(2t)

\int 3 sin (2 t) d t

tangent f(x)=4x^2-4x+1,\at x=1

t an g e n t f (x) = 4 x^{2} - 4 x + 1, at x = 1

tangent f(x)=((x+2)/(x-2))^2,\at x=6

t an g e n t f (x) = (\frac{x + 2}{x - 2})^{2}, at x = 6

f^'(x)= 1/((1-x^2)^2)

f^{^{'}} (x) = \frac{1}{( 1 - x ^{2} ) ^{2}}

derivative of 2x^{1/4}(x^3-11)

\frac{d}{d x} (2 x^{\frac{1}{4}} (x^{3} - 11))