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人気のある微分積分 >

(\partial)/(\partial x)(xy^7-x^2y)

解

\frac{\partial}{\partial x} (x y^{7} - x^{2} y)

解

y^{7} - 2 y x

解答ステップ

\frac{\partial}{\partial x} (x y^{7} - x^{2} y)

y

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 x} (x y^{7}) - \frac{\partial}{\partial x} (x^{2} y)

\frac{\partial}{\partial x} (x y^{7}) = y^{7}

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

= y^{7} - 2 y x

人気の例

derivative of (x^2/(4x+1))

\frac{d}{d x} (\frac{x ^{2}}{4 x + 1})

derivative f(x)=(2-x^2)/(3+x^2)

d er i v a t i v e f (x) = \frac{2 - x ^{2}}{3 + x ^{2}}

sum from n=1 to infinity of arctan(18n)

n = 1 \sum \infty arctan (18 n)

sum from n=0 to infinity of (1.1)^n

n = 0 \sum \infty (1.1)^{n}

derivative y=arctan(x^2+1)

d er i v a t i v e y = arctan (x^{2} + 1)