derivative of cos(xy-3y^4+3)

Lösung

\frac{d}{d x} (cos (x y) - 3 y^{4} + 3)

- sin (x y) (x \frac{d y}{d x} + y) - 12 y^{3} \frac{d y}{d x}

Schritte zur Lösung

\frac{d}{d x} (cos (x y) - 3 y^{4} + 3)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (cos (x y)) - \frac{d}{d x} (3 y^{4}) + \frac{d}{d x} (3)

\frac{d}{d x} (cos (x y)) = - sin (x y) (y + x \frac{d y}{d x})

\frac{d}{d x} (3 y^{4}) = 12 y^{3} \frac{d y}{d x}

\frac{d}{d x} (3) = 0

= - sin (x y) (y + x \frac{d y}{d x}) - 12 y^{3} \frac{d y}{d x} + 0

Vereinfache

= - sin (x y) (x \frac{d y}{d x} + y) - 12 y^{3} \frac{d y}{d x}

\frac{\partial}{\partial x} (\frac{A}{x + 5 x})

\frac{d}{d x} ((1 + x) (x^{3}))

\frac{\partial}{\partial y} (x^{\frac{1}{3}} y^{\frac{2}{3}})

\int \frac{x ^{2} + 6 x + 2}{x ^{3} + 9 x ^{2} + 6 x + 9} d x

y^{^{'}} + 0.06 y = 6