derivative of sqrt(x^2+x+3)

解答

\frac{d}{d x} (x^{2} + x + 3)

\frac{2 x + 1}{2 x ^{2} + x + 3}

求解步骤

\frac{d}{d x} (x^{2} + x + 3)

使用连锁律:

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

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

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

= \frac{1}{2 x ^{2} + x + 3} (2 x + 1)

化简

\frac{1}{2 x ^{2} + x + 3} (2 x + 1) : \frac{2 x + 1}{2 x ^{2} + x + 3}

= \frac{2 x + 1}{2 x ^{2} + x + 3}

(x^{4} + y^{2}) d x - x y d y = 0

\int (tan (θ)) d θ

x \to 0 lim (\frac{sin ( π x )}{x})

\int \frac{1}{x ( ln ( x ) ) ^{5}} d x

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{5}{x ^{4}}) (x + 3 x^{3}))