(\partial ^2)/(\partial x^2)(e^{3x+4y}cos(5z))

解答

\frac{\partial ^{2}}{\partial x ^{2}} (e^{3 x + 4 y} cos (5 z))

9 e^{3 x + 4 y} cos (5 z)

求解步骤

\frac{\partial ^{2}}{\partial x ^{2}} (e^{3 x + 4 y} cos (5 z))

\frac{\partial}{\partial x} (e^{3 x + 4 y} cos (5 z)) = cos (5 z) e^{3 x + 4 y} \cdot 3

= \frac{\partial}{\partial x} (cos (5 z) e^{3 x + 4 y} \cdot 3)

\frac{\partial}{\partial x} (cos (5 z) e^{3 x + 4 y} \cdot 3) = 9 e^{3 x + 4 y} cos (5 z)

= 9 e^{3 x + 4 y} cos (5 z)