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

الحلّ

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

e^{y^{2} x + z^{2}} y^{4}

خطوات الحلّ

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

كثوابت

y, z

تعامل مع

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

:استخرج الثابت

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

استعمل قانون السلسلة:

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

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

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

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

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

بسّط:

e^{y^{2} x + z^{2}} y^{4}

= e^{y^{2} x + z^{2}} y^{4}

y^{^{'}} = x^{2} e^{2 y}, y (- 1) = - 1

\frac{d}{d t} (3 cos (t) - 2 e^{2 t})

s l o p e in t erce pt (- 1, 0), (0, - 2)

(x^{2} + 3 x y + y^{2}) d x - x^{2} d y = 0

t a y l or cos (x), - \frac{π}{2}