derivative of (1+cos(x)sin(x))

Lösung

\frac{d}{d x} ((1 + cos (x)) sin (x))

- sin^{2} (x) + cos (x) (1 + cos (x))

Schritte zur Lösung

\frac{d}{d x} ((1 + cos (x)) sin (x))

Wende die Produktregel an:

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

f = 1 + cos (x), g = sin (x)

= \frac{d}{d x} (1 + cos (x)) sin (x) + \frac{d}{d x} (sin (x)) (1 + cos (x))

\frac{d}{d x} (1 + cos (x)) = - sin (x)

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

= (- sin (x)) sin (x) + cos (x) (1 + cos (x))

Vereinfache

(- sin (x)) sin (x) + cos (x) (1 + cos (x)) : - sin^{2} (x) + cos (x) (1 + cos (x))

= - sin^{2} (x) + cos (x) (1 + cos (x))

\frac{\partial}{\partial x} (\frac{1}{5 x ^{4}})

in v erse l a pl a ce \frac{4}{( s + 2 ) ^{3}}

x \to 0 lim ((3 x + 1))

d er i v a t i v e f (x) = lo g_{10} (x)

\int \frac{x ^{2} + 2 x + 4}{( x + 1 ) ^{3}} d x