derivative of 2sin^2(x+5sin(x)-3)

解答

\frac{d}{d x} (2 sin^{2} (x) + 5 sin (x) - 3)

2 sin (2 x) + 5 cos (x)

求解步骤

\frac{d}{d x} (2 sin^{2} (x) + 5 sin (x) - 3)

使用微分加减法定则:

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

= \frac{d}{d x} (2 sin^{2} (x)) + \frac{d}{d x} (5 sin (x)) - \frac{d}{d x} (3)

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

\frac{d}{d x} (5 sin (x)) = 5 cos (x)

\frac{d}{d x} (3) = 0

= 2 sin (2 x) + 5 cos (x) - 0

化简

= 2 sin (2 x) + 5 cos (x)

\frac{d}{d x} (\frac{x}{e ^{2 x}})

y^{^{'}} + 8 x^{2} y = x^{2}

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

s l o p e (0, 0), (4, 2)

\int \frac{cos ( t )}{5 + sin ( t )} d t