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

Lösung

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

cos (x) + sin (2 x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

cos (x) sin (x) + cos (x) (1 + sin (x)) : cos (x) + sin (2 x)

= cos (x) + sin (2 x)

y^{^{'}} = (x - 1) e^{x}

d er i v a t i v e \frac{0.3 ( 9 ^{x} )}{x ^{3}}

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

\frac{d y}{d x} - y = \frac{e ^{x}}{y}

\frac{\partial}{\partial x} ((x^{2})^{- \frac{1}{2}})