derivative f(x)=tan(x)sin(6x^3)

解答

导数

f (x) = tan (x) sin (6 x^{3})

sec^{2} (x) sin (6 x^{3}) + cos (6 x^{3}) \cdot 18 x^{2} tan (x)

求解步骤

\frac{d}{d x} (tan (x) sin (6 x^{3}))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = tan (x), g = sin (6 x^{3})

= \frac{d}{d x} (tan (x)) sin (6 x^{3}) + \frac{d}{d x} (sin (6 x^{3})) tan (x)

\frac{d}{d x} (tan (x)) = sec^{2} (x)

\frac{d}{d x} (sin (6 x^{3})) = cos (6 x^{3}) \cdot 18 x^{2}

= sec^{2} (x) sin (6 x^{3}) + cos (6 x^{3}) \cdot 18 x^{2} tan (x)

\frac{d}{d x} (1 0^{x} - 1 0^{- x})

d er i v a t i v e f (x) = (x^{2} - \frac{2}{x})^{- 5}

x \to \infty lim (13 x (e^{\frac{1}{x}}) - 13 x)

y^{^{'}} = 8 - \frac{y}{200} 4, y (0) = 50

x \to \frac{π}{4} lim (sin (2 x))