derivative f(x)=sin^2(tan(sqrt(x)))

Lösung

ableitung von

f (x) = sin^{2} (tan (x))

\frac{sec ^{2} ( x ) cos ( tan ( x ) ) sin ( tan ( x ) )}{x}

Schritte zur Lösung

\frac{d}{d x} (sin^{2} (tan (x)))

Wende die Kettenregel an:

2 sin (tan (x)) \frac{d}{d x} (sin (tan (x)))

= 2 sin (tan (x)) \frac{d}{d x} (sin (tan (x)))

\frac{d}{d x} (sin (tan (x))) = \frac{sec ^{2} ( x ) cos ( tan ( x ) )}{2 x}

= 2 sin (tan (x)) \frac{sec ^{2} ( x ) cos ( tan ( x ) )}{2 x}

Vereinfache

2 sin (tan (x)) \frac{sec ^{2} ( x ) cos ( tan ( x ) )}{2 x} : \frac{sec ^{2} ( x ) cos ( tan ( x ) ) sin ( tan ( x ) )}{x}

= \frac{sec ^{2} ( x ) cos ( tan ( x ) ) sin ( tan ( x ) )}{x}

\frac{d}{d t} (- \frac{1}{t + 1})

d er i v a t i v e f (x) = \frac{x}{a}

t an g e n t f (x) = x^{2} (4 - x)^{2}, at x = 1

x \to \infty lim (\frac{12 x ^{3} - 4 x + 1}{1 + 3 x + 2 x ^{3}})

\int_{- 3}^{3} ∣ x ∣ - (x^{2} - 6) d x