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人気のある微分積分 >

derivative f(x)=x^2sin(x)

解

導関数

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

解

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

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

グラフ

人気の例

derivative of-x^3+9x^2-6x+9

\frac{d}{d x} (- x^{3} + 9 x^{2} - 6 x + 9)

derivative 8/(sqrt(64+64t^2))

d er i v a t i v e \frac{8}{64 + 64 t ^{2}}

(dy)/(dx)=2cos(x)(y+1),y(pi/6)=2

\frac{d y}{d x} = 2 cos (x) (y + 1), y (\frac{π}{6}) = 2

(\partial)/(\partial x)(2x^2y^2)

\frac{\partial}{\partial x} (2 x^{2} y^{2})

sum from n=0 to infinity of 9(3/4)^n

n = 0 \sum \infty 9 (\frac{3}{4})^{n}