derivative of (cos(2x)/(sin(3x)))

Lösung

\frac{d}{d x} (\frac{cos ( 2 x )}{sin ( 3 x )})

- 2 sin (2 x) csc (3 x) - 3 cot (3 x) csc (3 x) cos (2 x)

Schritte zur Lösung

\frac{d}{d x} (\frac{cos ( 2 x )}{sin ( 3 x )})

Vereinfache

\frac{cos ( 2 x )}{sin ( 3 x )} : cos (2 x) csc (3 x)

= \frac{d}{d x} (cos (2 x) csc (3 x))

Wende die Produktregel an:

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

f = cos (2 x), g = csc (3 x)

= \frac{d}{d x} (cos (2 x)) csc (3 x) + \frac{d}{d x} (csc (3 x)) cos (2 x)

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

\frac{d}{d x} (csc (3 x)) = - cot (3 x) csc (3 x) \cdot 3

= (- sin (2 x) \cdot 2) csc (3 x) + (- cot (3 x) csc (3 x) \cdot 3) cos (2 x)

Vereinfache

= - 2 sin (2 x) csc (3 x) - 3 cot (3 x) csc (3 x) cos (2 x)

\int_{0}^{16} t^{2} + 2 t + 1 d t

y^{^{'}} = \frac{( x ^{3} y ^{3} + 4 x ^{3} )}{y ^{2}}

\int_{\frac{1}{5}}^{3} 12 x ln (5 x) d x

\int (x^{2} + x + \frac{1}{x}) d x

d er i v a t i v e f (x) = 5 x^{2} - 5 x + 9