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人気のある微分積分 >

derivative of xcos(4x)

解

\frac{d}{d x} (x cos (4 x))

解

cos (4 x) - 4 x sin (4 x)

解答ステップ

\frac{d}{d x} (x cos (4 x))

積の法則を適用:

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

f = x, g = cos (4 x)

= \frac{d x}{d x} cos (4 x) + \frac{d}{d x} (cos (4 x)) x

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

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

= 1 \cdot cos (4 x) + (- sin (4 x) \cdot 4) x

簡素化

= cos (4 x) - 4 x sin (4 x)

グラフ

人気の例

(x^2+1)y^'+9x(y-1)=0,y(0)=4

(x^{2} + 1) y^{^{'}} + 9 x (y - 1) = 0, y (0) = 4

y+2t^2+y^'tln(t)=0

y + 2 t^{2} + y^{^{'}} t ln (t) = 0

integral of (x+8)/(x^2+16)

\int \frac{x + 8}{x ^{2} + 16} d x

(\partial)/(\partial y)(3x^2-2xy+2)

\frac{\partial}{\partial y} (3 x^{2} - 2 x y + 2)

(\partial)/(\partial x)(ln((3xy)/(5z)))

\frac{\partial}{\partial x} (ln (\frac{3 x y}{5 z}))