(\partial)/(\partial x)(4cos(x^2+y^2))

Lösung

\frac{\partial}{\partial x} (4 cos (x^{2} + y^{2}))

- 8 x sin (x^{2} + y^{2})

Schritte zur Lösung

\frac{\partial}{\partial x} (4 cos (x^{2} + y^{2}))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 4 \frac{\partial}{\partial x} (cos (x^{2} + y^{2}))

Wende die Kettenregel an:

- sin (x^{2} + y^{2}) \frac{\partial}{\partial x} (x^{2} + y^{2})

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

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

= 4 (- sin (x^{2} + y^{2}) \cdot 2 x)

Vereinfache

= - 8 x sin (x^{2} + y^{2})

l a pl a ce t r an s f or m e^{t} cos (6 t)

t an g e n t 5 - x^{2}

d er i v a t i v e f (x) = ln (x^{2} + 3)

d er i v a t i v e y = (x + 1) (x + 2)

x^{2} y^{^{'}} = y^{2} + 5 x y + 4 x^{2}