(\partial)/(\partial x)(3xcos(5xy))

פתרון

\frac{\partial}{\partial x} (3 x cos (5 x y))

3 (cos (5 x y) - 5 x y sin (5 x y))

צעדי פתרון

\frac{\partial}{\partial x} (3 x cos (5 x y))

כאל קבוע

y

התייחס ל

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

:הוצא את הקבוע

= 3 \frac{\partial}{\partial x} (x cos (5 x y))

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

:השתמש בחוק הכפל

f = x, g = cos (5 x y)

= 3 (\frac{\partial}{\partial x} (x) cos (5 x y) + \frac{\partial}{\partial x} (cos (5 x y)) x)

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

\frac{\partial}{\partial x} (cos (5 x y)) = - sin (5 x y) \cdot 5 y

= 3 (1 \cdot cos (5 x y) + (- sin (5 x y) \cdot 5 y) x)

פשט

= 3 (cos (5 x y) - 5 x y sin (5 x y))

\frac{1}{2} (x^{4} + 7)

\int e^{x} 0.2 d x

f (x) = x^{3} - 2 x^{2} - 6 x + 6, at x = 0

\int (3 x)^{2} d x

\frac{d}{d x} (- x y^{3})