derivative of (3^x/(tan(x)))

Lösung

\frac{d}{d x} (\frac{3 ^{x}}{tan ( x )})

ln (3) \cdot 3^{x} cot (x) - 3^{x} csc^{2} (x)

Schritte zur Lösung

\frac{d}{d x} (\frac{3 ^{x}}{tan ( x )})

Vereinfache

\frac{3 ^{x}}{tan ( x )} : 3^{x} cot (x)

= \frac{d}{d x} (3^{x} cot (x))

Wende die Produktregel an:

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

f = 3^{x}, g = cot (x)

= \frac{d}{d x} (3^{x}) cot (x) + \frac{d}{d x} (cot (x)) 3^{x}

\frac{d}{d x} (3^{x}) = 3^{x} ln (3)

\frac{d}{d x} (cot (x)) = - csc^{2} (x)

= 3^{x} ln (3) cot (x) + (- csc^{2} (x)) \cdot 3^{x}

Vereinfache

= ln (3) \cdot 3^{x} cot (x) - 3^{x} csc^{2} (x)

\frac{d}{d x} (x^{7} e^{9 x})

n = 2 \sum \infty \frac{8}{( n ^{2} - 1 )}

\int (4 sin (x) - 1 + 8 x^{- 5}) d x

\int t^{2} - 4 t + 3 d t

\int_{1}^{8} x ln (x) d x