derivative f(x)=sec(x)tan(x)

Lösung

ableitung von

f (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{d}{d x} (- 4 cos (x) + sin (x))

t an g e n t f (x) = \frac{x}{( 4 x - 3 ) ^{8}}, at x = 1

a re a 8 - 2 x, x^{3} - 7 x^{2} + 12 x, 1, 4

\int \frac{x ^{4} + x + 1}{x ^{3} - x} d x

y^{^{'}} - y = 2 x