d/(da)(2sin^2(a)cos^2(a))

解答

\frac{d}{d a} (2 sin^{2} (a) cos^{2} (a))

2 sin (2 a) cos (2 a)

求解步骤

\frac{d}{d a} (2 sin^{2} (a) cos^{2} (a))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d a} (sin^{2} (a) cos^{2} (a))

使用微分乘法定则:

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

f = sin^{2} (a), g = cos^{2} (a)

= 2 (\frac{d}{d a} (sin^{2} (a)) cos^{2} (a) + \frac{d}{d a} (cos^{2} (a)) sin^{2} (a))

\frac{d}{d a} (sin^{2} (a)) = sin (2 a)

\frac{d}{d a} (cos^{2} (a)) = - sin (2 a)

= 2 (sin (2 a) cos^{2} (a) + (- sin (2 a)) sin^{2} (a))

化简

2 (sin (2 a) cos^{2} (a) + (- sin (2 a)) sin^{2} (a)) : 2 sin (2 a) cos (2 a)

= 2 sin (2 a) cos (2 a)

d er i v a t i v e f (x) = x^{3} sin^{2} (x)

d er i v a t i v e e^{3 x} \cdot sin (ln (x))

d er i v a t i v e 4 t^{2} + 3 t + 3

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

\frac{d}{d x} (a \cdot e^{2 x} + b \cdot e^{- 3 x} + c \cdot e^{x})