derivative f(x)=(x^2)/(cos(x))

Lösung

ableitung von

f (x) = \frac{x ^{2}}{cos ( x )}

2 x sec (x) + sec (x) tan (x) x^{2}

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Produktregel an:

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

f = x^{2}, g = sec (x)

= \frac{d}{d x} (x^{2}) sec (x) + \frac{d}{d x} (sec (x)) x^{2}

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

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

= 2 x sec (x) + sec (x) tan (x) x^{2}

d er i v a t i v e f (x) = tan (5 x)

\int sec^{- \frac{1}{2}} (x) tan^{3} (x) d x

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

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

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