derivative of cos(2x*sin(2x))

Lösung

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

2 cos (4 x)

Schritte zur Lösung

\frac{d}{d x} (cos (2 x) sin (2 x))

Wende die Produktregel an:

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

f = cos (2 x), g = sin (2 x)

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

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

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

= (- sin (2 x) \cdot 2) sin (2 x) + cos (2 x) \cdot 2 cos (2 x)

Vereinfache

(- sin (2 x) \cdot 2) sin (2 x) + cos (2 x) \cdot 2 cos (2 x) : 2 cos (4 x)

= 2 cos (4 x)

\int \frac{6}{x ^{5}} d x

x \to - 7 - lim (x^{2} + \frac{4}{x + 7})

x \to 2 lim (3 x^{2} - 4 x + 6)

y^{^{'}} = 8 x + y

\frac{d y}{d x} + y = 2 x^{2}