derivative of cosh(xcos(x^2))

Lösung

\frac{d}{d x} (cosh (x) cos (x^{2}))

sinh (x) cos (x^{2}) - 2 x sin (x^{2}) cosh (x)

Schritte zur Lösung

\frac{d}{d x} (cosh (x) cos (x^{2}))

Wende die Produktregel an:

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

f = cosh (x), g = cos (x^{2})

= \frac{d}{d x} (cosh (x)) cos (x^{2}) + \frac{d}{d x} (cos (x^{2})) cosh (x)

\frac{d}{d x} (cosh (x)) = sinh (x)

\frac{d}{d x} (cos (x^{2})) = - sin (x^{2}) \cdot 2 x

= sinh (x) cos (x^{2}) + (- sin (x^{2}) \cdot 2 x) cosh (x)

Vereinfache

= sinh (x) cos (x^{2}) - 2 x sin (x^{2}) cosh (x)

\frac{d}{d x} (arctan (\frac{8}{x}))

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

a re a y = - x^{2} + 16, y = \frac{- x}{4} - 1, 4 (y + 6.5) = 6.5 x

d er i v a t i v e (3 x^{2} - 6 x + 6) e^{- 5 x}

\int_{0}^{2} sin^{2} (x co) s^{2} 2 x