derivative of arctan({g}(x)(x))

Lösung

\frac{d}{d x} (arctan (g (x)) (x))

\frac{x \frac{d}{d x} ( g ( x ) )}{g ( x ) ^{2} + 1} + arctan (g (x))

Schritte zur Lösung

\frac{d}{d x} (arctan (g (x)) (x))

Wende die Produktregel an:

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

f = arctan (g (x)), g = x

= \frac{d}{d x} (arctan (g (x))) x + \frac{d x}{d x} arctan (g (x))

\frac{d}{d x} (arctan (g (x))) = \frac{\frac{d}{d x} ( g ( x ) )}{g ( x ) ^{2} + 1}

\frac{d x}{d x} = 1

= \frac{\frac{d}{d x} ( g ( x ) )}{g ( x ) ^{2} + 1} x + 1 \cdot arctan (g (x))

Vereinfache

\frac{\frac{d}{d x} ( g ( x ) )}{g ( x ) ^{2} + 1} x + 1 \cdot arctan (g (x)) : \frac{x \frac{d}{d x} ( g ( x ) )}{g ( x ) ^{2} + 1} + arctan (g (x))

= \frac{x \frac{d}{d x} ( g ( x ) )}{g ( x ) ^{2} + 1} + arctan (g (x))

\frac{\partial}{\partial x} (3 sin (\frac{6 x}{y}))

x \to - \infty lim (\frac{5 + 2 x}{9 + 4 x ^{2}})

t an g e n t 2 x + 1, at x = \frac{1}{4}

n = 1 \sum \infty e^{- n} n!

f (x) = 8^{x}