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人気のある微分積分 >

derivative of x^6e^{5x}

解

\frac{d}{d x} (x^{6} e^{5 x})

解

6 x^{5} e^{5 x} + e^{5 x} \cdot 5 x^{6}

解答ステップ

\frac{d}{d x} (x^{6} e^{5 x})

積の法則を適用:

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

f = x^{6}, g = e^{5 x}

= \frac{d}{d x} (x^{6}) e^{5 x} + \frac{d}{d x} (e^{5 x}) x^{6}

\frac{d}{d x} (x^{6}) = 6 x^{5}

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

= 6 x^{5} e^{5 x} + e^{5 x} \cdot 5 x^{6}

グラフ

人気の例

limit as x approaches 0 of ((x^2))/(x-1)

x \to 0 lim (\frac{( x ^{2} )}{x - 1})

tangent y= 1/(x^3),(2, 1/8)

t an g e n t y = \frac{1}{x ^{3}}, (2, \frac{1}{8})

derivative of 5+4x

\frac{d}{d x} (5 + 4 x)

(\partial)/(\partial y)(cos(2x)sin(3y))

\frac{\partial}{\partial y} (cos (2 x) sin (3 y))

25y^{''}-40y^'+16y=0,y(4)=2,y^'(4)=2

25 y^{^{''}} - 40 y^{^{'}} + 16 y = 0, y (4) = 2, y^{^{'}} (4) = 2