(\partial)/(\partial x)(ax^3+xe^x-1)

الحلّ

\frac{\partial}{\partial x} (a x^{3} + x e^{x} - 1)

3 a x^{2} + e^{x} x + e^{x}

خطوات الحلّ

\frac{\partial}{\partial x} (a x^{3} + x e^{x} - 1)

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

:استعمل قانون الجمع

= \frac{\partial}{\partial x} (a x^{3}) + \frac{\partial}{\partial x} (x e^{x}) - \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (a x^{3}) = 3 a x^{2}

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

\frac{\partial}{\partial x} (1) = 0

= 3 a x^{2} + e^{x} + e^{x} x - 0

بسّط

= 3 a x^{2} + e^{x} x + e^{x}

\int \frac{x ^{2} + 24}{x ( x - 2 ) ^{3}} d x

\frac{d}{d x} (\frac{e ^{x}}{7 + e ^{x}})

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

cos (2 arctan (x))

\int sin (5 x + \frac{π}{6}) d x