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受欢迎的微积分 >

derivative of-4sin^2(x+4sin^2(x+pi/3))

解答

\frac{d}{d x} (- 4 \cdot sin^{2} (x) + 4 \cdot sin^{2} (x + \frac{π}{3}))

解答

- 6 sin (2 x) + 23 cos (2 x)

求解步骤

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

化简

- 4 sin^{2} (x) + 4 sin^{2} (x + \frac{π}{3}) : 3 cos^{2} (x) - 3 sin^{2} (x) + 3 sin (2 x)

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

使用微分加减法定则:

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

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

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

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

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

= - 3 sin (2 x) - 3 sin (2 x) + 3 cos (2 x) \cdot 2

化简

= - 6 sin (2 x) + 23 cos (2 x)

作图

流行的例子

tangent f(x)=0.6831x^{-1.031},\at x=1

t an g e n t f (x) = 0.6831 x^{- 1.031}, at x = 1

(\partial)/(\partial x)((1/x+1/y)^{-1})

\frac{\partial}{\partial x} ((\frac{1}{x} + \frac{1}{y})^{- 1})

cos(x)(dy)/(dx)+sin(x)y=1

cos (x) \frac{d y}{d x} + sin (x) y = 1

integral of x^3-1/2

\int x^{3} - \frac{1}{2} d x

integral of x*cos((pix)/2)

\int x \cdot cos (\frac{π x}{2}) d x