derivative of-cos(cos(x)sin(x))

Lösung

\frac{d}{d x} (- cos (cos (x)) sin (x))

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

Schritte zur Lösung

\frac{d}{d x} (- cos (cos (x)) sin (x))

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = cos (cos (x)), g = sin (x)

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

\frac{d}{d x} (cos (cos (x))) = sin (cos (x)) sin (x)

\frac{d}{d x} (sin (x)) = cos (x)

= - (sin (cos (x)) sin (x) sin (x) + cos (x) cos (cos (x)))

Vereinfache

- (sin (cos (x)) sin (x) sin (x) + cos (x) cos (cos (x))) : - sin^{2} (x) sin (cos (x)) - cos (x) cos (cos (x))

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

\int x^{3} sin^{2} (x) d x

\int_{\frac{π}{4}}^{\frac{π}{3}} 1

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

x y^{^{'}} + y = e^{x}, y (- 1) = 4

\frac{d}{d r} (π r^{2} h)