derivative of (x^{sin(x})/(cos(x)))

Lösung

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

x^{s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x}) sec (x) + sec (x) tan (x) x^{s i n (x)}

Schritte zur Lösung

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

Vereinfache

\frac{x ^{s i n (x)}}{cos ( x )} : x^{s i n (x)} sec (x)

= \frac{d}{d x} (x^{s i n (x)} sec (x))

Wende die Produktregel an:

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

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

= \frac{d}{d x} (x^{s i n (x)}) sec (x) + \frac{d}{d x} (sec (x)) x^{s i n (x)}

\frac{d}{d x} (x^{s i n (x)}) = x^{s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

= x^{s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x}) sec (x) + sec (x) tan (x) x^{s i n (x)}

x \to 2 + lim (\frac{x - 2}{∣ x - 2 ∣})

x e^{x} ln (y + 1) d x + (x + 1)^{2} (\frac{1}{y + 1}) d y = 0

\int \frac{( 3 sin ^{3} ( x ) )}{cos ( x )} d x

\int (x^{3} + 3)^{\frac{1}{4}} \cdot x^{5} d x

l a pl a ce t r an s f or m t e^{- 3 t} cos (2 t)