derivative of sec(xtan(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (2 y ln (x))

\int 4 x^{3} e^{- x^{2}} d x

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

\int sin^{3} (x) cos^{18} (x) d x

\frac{d}{d x} (\frac{( x ^{3} + y ^{3} )}{( x ^{2} + y ^{2} )})