derivative of 9xsin(x^2)

解答

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

9 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

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

f = x, g = sin (x^{2})

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

\frac{d x}{d x} = 1

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

= 9 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx)

化简

9 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx) : 9 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

= 9 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

y^{^{''}} + 9 y^{^{'}} = 0

y^{^{'}} = 3 x^{2} y - 8 e^{(x^{3} - 4 x)}

y^{^{''}} + 4 π^{2} y = cos^{3} (2 π x), y (0) = 1

t an g e n t f (x) = 5 - 5 x^{2}, (5, - 120)

x \to 5 lim (x^{2} + 2 x - 4)