derivative of x^2sec(1/(x^3))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = sec (\frac{1}{x ^{3}})

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

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

\frac{d}{d x} (sec (\frac{1}{x ^{3}})) = - \frac{3 sec ( \frac{1}{x ^{3}} ) tan ( \frac{1}{x ^{3}} )}{x ^{4}}

= 2 x sec (\frac{1}{x ^{3}}) + (- \frac{3 sec ( \frac{1}{x ^{3}} ) tan ( \frac{1}{x ^{3}} )}{x ^{4}}) x^{2}

Vereinfache

2 x sec (\frac{1}{x ^{3}}) + (- \frac{3 sec ( \frac{1}{x ^{3}} ) tan ( \frac{1}{x ^{3}} )}{x ^{4}}) x^{2} : 2 x sec (\frac{1}{x ^{3}}) - \frac{3 sec ( \frac{1}{x ^{3}} ) tan ( \frac{1}{x ^{3}} )}{x ^{2}}

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

\int \frac{x ^{3}}{x ^{8} + 5} d x

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

in v erse l a pl a ce \frac{s + 1}{( s + 6 ) ^{2} \cdot ( s + 2 )}

\frac{d}{d x} (- e^{x - 28} + 75)

\int - x - 2 d x