derivative x^4sec(5/x)

Lösung

ableitung von

x^{4} sec (\frac{5}{x})

4 x^{3} sec (\frac{5}{x}) - 5 x^{2} sec (\frac{5}{x}) tan (\frac{5}{x})

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{4}, g = sec (\frac{5}{x})

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (sec (\frac{5}{x})) = - \frac{5 sec ( \frac{5}{x} ) tan ( \frac{5}{x} )}{x ^{2}}

= 4 x^{3} sec (\frac{5}{x}) + (- \frac{5 sec ( \frac{5}{x} ) tan ( \frac{5}{x} )}{x ^{2}}) x^{4}

Vereinfache

4 x^{3} sec (\frac{5}{x}) + (- \frac{5 sec ( \frac{5}{x} ) tan ( \frac{5}{x} )}{x ^{2}}) x^{4} : 4 x^{3} sec (\frac{5}{x}) - 5 x^{2} sec (\frac{5}{x}) tan (\frac{5}{x})

= 4 x^{3} sec (\frac{5}{x}) - 5 x^{2} sec (\frac{5}{x}) tan (\frac{5}{x})

z \to 0 lim (\frac{1}{f ( z ) \frac{1}{z}})

d er i v a t i v e x + 4

n = 1 \sum \infty n \cdot sin (π \cdot n)

\int \frac{ln ( ln ( 5 x ) )}{5 x} d x

d er i v a t i v e (x^{2} + 6)^{9}