derivative of 2+4cos(x^3+3sin(x^3))

解答

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

9 x^{2} cos (x^{3}) - 12 x^{2} sin (x^{3})

求解步骤

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

使用微分加减法定则:

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

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

\frac{d}{d x} (2) = 0

\frac{d}{d x} (4 cos (x^{3})) = - 12 x^{2} sin (x^{3})

\frac{d}{d x} (3 sin (x^{3})) = 9 x^{2} cos (x^{3})

= 0 - 12 x^{2} sin (x^{3}) + 9 x^{2} cos (x^{3})

化简

= 9 x^{2} cos (x^{3}) - 12 x^{2} sin (x^{3})

\frac{d}{d x} (ln (4 \frac{x - 1}{x + 1}))

d er i v a t i v e f (x) = \frac{1}{5} x^{2} + \frac{200000}{x}

(1 + x^{2}) y^{^{''}} + y^{^{'}} x + a x = 0

f (t) = 3 cos (t)

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