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人気のある微分積分 >

(\partial)/(\partial y)(x^2+5y^2)

解

\frac{\partial}{\partial y} (x^{2} + 5 y^{2})

解

10 y

解答ステップ

\frac{\partial}{\partial y} (x^{2} + 5 y^{2})

x

を定数として扱う

和/差の法則を適用:

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

= \frac{\partial}{\partial y} (x^{2}) + \frac{\partial}{\partial y} (5 y^{2})

\frac{\partial}{\partial y} (x^{2}) = 0

\frac{\partial}{\partial y} (5 y^{2}) = 10 y

= 0 + 10 y

簡素化

= 10 y

人気の例

limit as x approaches 3-of-3/7 x+4/11

x \to 3 - lim (- \frac{3}{7} x + \frac{4}{11})

(\partial)/(\partial z)(x/(sqrt(y+z)))

\frac{\partial}{\partial z} (\frac{x}{y + z})

limit as x approaches 0-of ((x+4))/((3))

x \to 0 - lim (\frac{( x + 4 )}{( 3 )})

9y^{''}-30y^'+25y=0

9 y^{^{''}} - 30 y^{^{'}} + 25 y = 0

integral of 2/5 x^{5/2}-54/5

\int \frac{2}{5} x^{\frac{5}{2}} - \frac{54}{5} d x