derivative f(x)=2x^3+4x^2+6x

解答

导数

f (x) = 2 x^{3} + 4 x^{2} + 6 x

6 x^{2} + 8 x + 6

求解步骤

\frac{d}{d x} (2 x^{3} + 4 x^{2} + 6 x)

使用微分加减法定则:

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

= \frac{d}{d x} (2 x^{3}) + \frac{d}{d x} (4 x^{2}) + \frac{d}{d x} (6 x)

\frac{d}{d x} (2 x^{3}) = 6 x^{2}

\frac{d}{d x} (4 x^{2}) = 8 x

\frac{d}{d x} (6 x) = 6

= 6 x^{2} + 8 x + 6

x \to 0 + lim (sin (\frac{5 π}{6} e^{x}))

\int (x + 1) [ln (x + 1) + c] d x

y^{2} y^{^{'}} = y^{2}

t an g e n t f (x) = x^{2} - 2 x

\int \frac{x ^{3}}{x ^{2} + 9} d x