derivative of xsec(xtan(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (sec (x) tan (x)) = - sec (x) + 2 sec^{3} (x)

= 1 \cdot sec (x) tan (x) + (- sec (x) + 2 sec^{3} (x)) x

Vereinfache

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

d er i v a t i v e f (x) = x + \frac{9}{x}

\frac{\partial}{\partial x} ((x y)^{z})

\int \frac{x ^{3} - x ^{2} - 4 x + 4}{x ^{3} - x ^{2} - 6 x} d x

\frac{\partial}{\partial x} (e^{2 y} cos (3 x))

in v erse l a pl a ce 3