derivative of 2cos(3x+2sin(10y)+3x-10y)

解答

\frac{d}{d x} (2 cos (3 x) + 2 sin (10 y) + 3 x - 10 y)

- 6 sin (3 x) + 20 cos (10 y) \frac{d y}{d x} + 3 - 10 \frac{d y}{d x}

求解步骤

\frac{d}{d x} (2 cos (3 x) + 2 sin (10 y) + 3 x - 10 y)

使用微分加减法定则:

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

= \frac{d}{d x} (2 cos (3 x)) + \frac{d}{d x} (2 sin (10 y)) + \frac{d}{d x} (3 x) - \frac{d}{d x} (10 y)

\frac{d}{d x} (2 cos (3 x)) = - 6 sin (3 x)

\frac{d}{d x} (2 sin (10 y)) = 20 cos (10 y) \frac{d y}{d x}

\frac{d}{d x} (3 x) = 3

\frac{d}{d x} (10 y) = 10 \frac{d y}{d x}

= - 6 sin (3 x) + 20 cos (10 y) \frac{d y}{d x} + 3 - 10 \frac{d y}{d x}

d er i v a t i v e \frac{( x ^{2} + 3 )}{( x + 1 )}

d er i v a t i v e 2 tan (x) + sec (x) - 3 cot (x)

d er i v a t i v e \frac{x ^{3}}{3 - 3 x}

d er i v a t i v e 3^{x} + 2

d er i v a t i v e lo g_{10} (\frac{2}{x})