derivative y=sqrt(x+\sqrt{x)}

解答

导数

y = x + x

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

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

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

n = 0 \sum \infty \frac{4 ^{(2 n + 1)}}{( - 4 ) ^{n}}

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

\int \frac{2 ^{t a n (x)}}{cos ^{2} ( x )} d x

x \to - 6 lim (\frac{x ^{2} - 2}{6 - x})