derivative of sec(xtan(x)(sqrt(x))(x+1))

Lösung

\frac{d}{d x} (sec (x) tan (x) (x) (x + 1))

x tan^{2} (x) sec (x) (x + 1) + sec (x) (x sec^{2} (x) (x + 1) + \frac{tan ( x ) ( 3 x + 1 )}{2 x})

Schritte zur Lösung

\frac{d}{d x} (sec (x) tan (x) (x) (x + 1))

Wende die Produktregel an:

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

f = sec (x), g = tan (x) x (x + 1)

= \frac{d}{d x} (sec (x)) tan (x) x (x + 1) + \frac{d}{d x} (tan (x) x (x + 1)) sec (x)

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

\frac{d}{d x} (tan (x) x (x + 1)) = x sec^{2} (x) (x + 1) + \frac{tan ( x ) ( 3 x + 1 )}{2 x}

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

sec (x) tan (x) tan (x) x (x + 1) = x tan^{2} (x) sec (x) (x + 1)

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

\frac{\partial}{\partial x} (8 x e^{x y})

n = 1 \sum \infty \frac{n !}{n 2 ^{n}}

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

\int x^{2} - 4 x + 7 d x

x \to - 1 lim (\frac{x ^{2} - 3}{1 - x})