derivative of (cos(x)(ln(tan(x))))

Lösung

\frac{d}{d x} ((cos (x)) (ln (tan (x))))

- sin (x) ln (tan (x)) + 2 csc (2 x) cos (x)

Schritte zur Lösung

\frac{d}{d x} ((cos (x)) (ln (tan (x))))

Wende die Produktregel an:

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

f = cos (x), g = ln (tan (x))

= \frac{d}{d x} (cos (x)) ln (tan (x)) + \frac{d}{d x} (ln (tan (x))) cos (x)

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

\frac{d}{d x} (ln (tan (x))) = 2 csc (2 x)

= (- sin (x)) ln (tan (x)) + 2 csc (2 x) cos (x)

Vereinfache

= - sin (x) ln (tan (x)) + 2 csc (2 x) cos (x)

t an g e n t (2 x + 3)^{\frac{1}{4}}

a re a y^{2} + 8 x = 16, y^{2} - 24 x = 48

d er i v a t i v e (8 x)^{2 x}

\frac{\partial}{\partial s} (\frac{s - 2 r}{t})

\int \frac{3 x + 1}{x} d x