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人気のある微分積分 >

derivative of sqrt(x+\sqrt{x+1)}

解

\frac{d}{d x} (x + x + 1)

解

\frac{2 x + 1 + 1}{4 x + 1 x + x + 1}

解答ステップ

\frac{d}{d x} (x + x + 1)

連鎖法則を適用:

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

= \frac{1}{2 x + x + 1} \frac{d}{d x} (x + x + 1)

\frac{d}{d x} (x + x + 1) = 1 + \frac{1}{2 x + 1}

= \frac{1}{2 x + x + 1} (1 + \frac{1}{2 x + 1})

簡素化

\frac{1}{2 x + x + 1} (1 + \frac{1}{2 x + 1}) : \frac{2 x + 1 + 1}{4 x + 1 x + x + 1}

= \frac{2 x + 1 + 1}{4 x + 1 x + x + 1}

グラフ

人気の例

面積 y=-x^2+16,y=(-x)/4-1,4(y+6.5)=6.5x

a re a y = - x^{2} + 16, y = \frac{- x}{4} - 1, 4 (y + 6.5) = 6.5 x

derivative (3x^2-6x+6)e^{-5x}

d er i v a t i v e (3 x^{2} - 6 x + 6) e^{- 5 x}

integral from 0 to 2 of sin^2(xco)s^22x

\int_{0}^{2} sin^{2} (x co) s^{2} 2 x

integral of 5/(4+9x^2)

\int \frac{5}{4 + 9 x ^{2}} d x

(\partial)/(\partial y)(sqrt(x^2+6xy+y^4))

\frac{\partial}{\partial y} (x^{2} + 6 x y + y^{4})