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Beliebt Rechnen >

(\partial)/(\partial x)(-3cos(pix)+6x^2y+5e^{xz}+3yz-98)

Lösung

\frac{\partial}{\partial x} (- 3 cos (π x) + 6 x^{2} y + 5 e^{x z} + 3 yz - 98)

Lösung

12 x y + 5 e^{x z} z + 3 π sin (π x)

Schritte zur Lösung

\frac{\partial}{\partial x} (- 3 cos (π x) + 6 x^{2} y + 5 e^{x z} + 3 yz - 98)

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

= - \frac{\partial}{\partial x} (3 cos (π x)) + \frac{\partial}{\partial x} (6 x^{2} y) + \frac{\partial}{\partial x} (5 e^{x z}) + \frac{\partial}{\partial x} (3 yz) - \frac{\partial}{\partial x} (98)

\frac{\partial}{\partial x} (3 cos (π x)) = - 3 π sin (π x)

\frac{\partial}{\partial x} (6 x^{2} y) = 12 y x

\frac{\partial}{\partial x} (5 e^{x z}) = 5 e^{x z} z

\frac{\partial}{\partial x} (3 yz) = 0

\frac{\partial}{\partial x} (98) = 0

= - (- 3 π sin (π x)) + 12 y x + 5 e^{x z} z + 0 - 0

Vereinfache

= 12 x y + 5 e^{x z} z + 3 π sin (π x)

Beliebte Beispiele

integral of x-8/x

\int x - \frac{8}{x} d x

taylor ln^2(1+x)

t a y l or ln^{2} (1 + x)

integral of 1/(sqrt(361-x^2))

\int \frac{1}{361 - x ^{2}} d x

(dy)/(dx)-y/x =xe^x,y(1)=e-1

\frac{d y}{d x} - \frac{y}{x} = x e^{x}, y (1) = e - 1

limit as x approaches infinity of 1/(4x)

x \to \infty lim (\frac{1}{4 x})