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(\partial)/(\partial x)(x^2y+e^{xy})

الحلّ

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

الحلّ

2 y x + e^{x y} y

خطوات الحلّ

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

كثابت

y

تعامل مع

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

:استعمل قانون الجمع

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

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

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

= 2 y x + e^{x y} y

أمثلة شائعة

(\partial ^3)/(\partial x\partial y\partial z)(e^{xyz^9})

\frac{\partial ^{3}}{\partial x \partial y \partial z} (e^{x y z^{9}})

\frac{d}{d t} (sin (t))

3xy^'-15y=x^{-4},y(1)=-2

3 x y^{^{'}} - 15 y = x^{- 4}, y (1) = - 2

integral from 0 to 4.5 of 90x

\int_{0}^{4.5} 90 x d x

derivative of 1+2tan(x)

\frac{d}{d x} (1 + 2 tan (x))