derivative of-7csc(x+1/(x^5))

Lösung

\frac{d}{d x} (- 7 csc (x) + \frac{1}{x ^{5}})

7 cot (x) csc (x) - \frac{5}{x ^{6}}

Schritte zur Lösung

\frac{d}{d x} (- 7 csc (x) + \frac{1}{x ^{5}})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (7 csc (x)) + \frac{d}{d x} (\frac{1}{x ^{5}})

\frac{d}{d x} (7 csc (x)) = - 7 cot (x) csc (x)

\frac{d}{d x} (\frac{1}{x ^{5}}) = - \frac{5}{x ^{6}}

= - (- 7 cot (x) csc (x)) - \frac{5}{x ^{6}}

Vereinfache

= 7 cot (x) csc (x) - \frac{5}{x ^{6}}

d er i v a t i v e arcsin (\frac{x}{a})

d er i v a t i v e (\frac{4}{3}) π x^{3}

\frac{d}{d x} (4 x y^{2} - x^{2} y^{2} - x y^{3})

\int - \frac{1}{2} x^{\frac{1}{2}} d x

t an g e n t f (x) = - 3 x^{2} + 3 x + 1, at x = 1