derivative 6cos(x)csc(x^2)

Lösung

ableitung von

6 cos (x) csc (x^{2})

6 (- sin (x) csc (x^{2}) - 2 x cot (x^{2}) csc (x^{2}) cos (x))

Schritte zur Lösung

\frac{d}{d x} (6 cos (x) csc (x^{2}))

Entferne die Konstante:

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

= 6 \frac{d}{d x} (cos (x) csc (x^{2}))

Wende die Produktregel an:

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

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

= 6 (\frac{d}{d x} (cos (x)) csc (x^{2}) + \frac{d}{d x} (csc (x^{2})) cos (x))

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

\frac{d}{d x} (csc (x^{2})) = - cot (x^{2}) csc (x^{2}) \cdot 2 x

= 6 ((- sin (x)) csc (x^{2}) + (- cot (x^{2}) csc (x^{2}) \cdot 2 x) cos (x))

Vereinfache

= 6 (- sin (x) csc (x^{2}) - 2 x cot (x^{2}) csc (x^{2}) cos (x))

l a pl a ce t r an s f or m cos (3 t + 5)

x \to - 2 + lim (2 x + 2 + x)

t an g e n t x^{2} + x + 4

y^{^{''}} - 3 y^{^{'}} + 7 y = 4 e^{3 t}

x \to 1 lim (3 x - 1)