derivative of sqrt(sec(x)*x^5)

Lösung

\frac{d}{d x} (sec (x) \cdot x^{5})

\frac{x ^{5} tan ( x ) sec ( x )}{2} + 5 x^{4} sec (x)

Schritte zur Lösung

\frac{d}{d x} (sec (x) x^{5})

Wende die Produktregel an:

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

f = sec (x), g = x^{5}

= \frac{d}{d x} (sec (x)) x^{5} + \frac{d}{d x} (x^{5}) sec (x)

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{tan ( x ) sec ( x )}{2} x^{5} + 5 x^{4} sec (x)

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x ^{5} tan ( x ) sec ( x )}{2} + 5 x^{4} sec (x)

\frac{\partial}{\partial x} (x + 2 y + z)

\int \frac{12 x + 30}{x ^{2} + 2 x - 8} d x

x \to 1 lim (e^{x^{2} + 7 x - 8})

x \to 2 lim (\frac{2}{x + 2})

\frac{d}{d x} (\frac{2 x}{5})