(\partial)/(\partial x)(e^{sin(x)}cos(x))

Lösung

\frac{\partial}{\partial x} (e^{s i n (x)} cos (x))

e^{s i n (x)} cos^{2} (x) - e^{s i n (x)} sin (x)

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{s i n (x)} cos (x))

Wende die Produktregel an:

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

f = e^{s i n (x)}, g = cos (x)

= \frac{\partial}{\partial x} (e^{s i n (x)}) cos (x) + \frac{\partial}{\partial x} (cos (x)) e^{s i n (x)}

\frac{\partial}{\partial x} (e^{s i n (x)}) = e^{s i n (x)} cos (x)

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

= e^{s i n (x)} cos (x) cos (x) + (- sin (x)) e^{s i n (x)}

Vereinfache

e^{s i n (x)} cos (x) cos (x) + (- sin (x)) e^{s i n (x)} : e^{s i n (x)} cos^{2} (x) - e^{s i n (x)} sin (x)

= e^{s i n (x)} cos^{2} (x) - e^{s i n (x)} sin (x)

f (x) = 7 x^{- 6} - 5 x^{- 3}

a re a y = x, (0, 1), x^{2}

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

\int \frac{1}{( x ^{2} + 21 ) ^{3}} d x

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