derivative f(x)=8x+sqrt(x^2+7x+3)

解答

导数

f (x) = 8 x + x^{2} + 7 x + 3

8 + \frac{2 x + 7}{2 x ^{2} + 7 x + 3}

求解步骤

\frac{d}{d x} (8 x + x^{2} + 7 x + 3)

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (8 x) + \frac{d}{d x} (x^{2} + 7 x + 3)

\frac{d}{d x} (8 x) = 8

\frac{d}{d x} (x^{2} + 7 x + 3) = \frac{2 x + 7}{2 x ^{2} + 7 x + 3}

= 8 + \frac{2 x + 7}{2 x ^{2} + 7 x + 3}

\int_{1}^{2} y^{3} + \frac{1}{4 y ^{3}} d y

ma c l a u r in ln (1 + 4 x^{2} + 4 x)

\frac{\partial}{\partial y} (e^{x y z^{5}} y z^{5})

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

\int 5 e^{3 x} d x