derivative derivative of tan(xsec(x))

Lösung

ableitung von

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

- sec (x) + 2 sec^{3} (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = tan (x), g = sec (x)

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

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

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

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

Vereinfache

sec^{2} (x) sec (x) + sec (x) tan (x) tan (x) : - sec (x) + 2 sec^{3} (x)

= - sec (x) + 2 sec^{3} (x)

d er i v a t i v e \frac{d}{d x} ((\frac{50}{( x )}) x)

h \to 0 lim \frac{( ( x + h ) ^{4} - x ^{4} )}{h}

d er i v a t i v e \frac{d}{d x} (\frac{100}{( 100 - x )})

s l o p e (4, 0), (0, 4)

\int (tan (y)) d y