derivative y=sec(tan(x))tan(sec(x))

Lösung

ableitung von

y = sec (tan (x)) tan (sec (x))

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

a re a y^{2} = x, x + y = 2

\int \frac{5 x ^{2} + x + 5}{( x ^{2} + 1 ) ^{2}} d x

\int 3 x - 1 d x

\frac{\partial}{\partial x} (ln (3 x + 4 y))

\frac{\partial}{\partial x} (x^{3} - 9 x y + y^{3} - 2)