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人気のある微分積分 >

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

解

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

解

y

解答ステップ

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

簡素化

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

= \frac{\partial}{\partial x} (x y)

y

を定数として扱う

定数を除去:

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

= y \frac{\partial}{\partial x} (x)

共通の導関数を適用:

\frac{\partial}{\partial x} (x) = 1

= y \cdot 1

簡素化

= y

人気の例

(f(x)(x)^{g(x)})'

(f (x) (x)^{g (x)})^{'}

limit as x approaches 2 of (4x^2-2x+5)/x

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

integral of (435)/(3x+14)-15

\int \frac{435}{3 x + 14} - 15 d x

tangent f(x)=3x^2+2x,\at x=3

t an g e n t f (x) = 3 x^{2} + 2 x, at x = 3

integral of (sin(x))/(sqrt(cos^3(x)))

\int \frac{sin ( x )}{cos ^{3} ( x )} d x