derivative of 2csc(pi/4 x+1)

Lösung

\frac{d}{d x} (2 csc (\frac{π}{4} x) + 1)

- \frac{π}{2} cot (\frac{π x}{4}) csc (\frac{π x}{4})

Schritte zur Lösung

\frac{d}{d x} (2 csc (\frac{π}{4} x) + 1)

Vereinfache

2 csc (\frac{π}{4} x) + 1 : 2 csc (\frac{π x}{4}) + 1

= \frac{d}{d x} (2 csc (\frac{π x}{4}) + 1)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (2 csc (\frac{π x}{4})) + \frac{d}{d x} (1)

\frac{d}{d x} (2 csc (\frac{π x}{4})) = - \frac{π}{2} cot (\frac{π x}{4}) csc (\frac{π x}{4})

\frac{d}{d x} (1) = 0

= - \frac{π}{2} cot (\frac{π x}{4}) csc (\frac{π x}{4}) + 0

Vereinfache

= - \frac{π}{2} cot (\frac{π x}{4}) csc (\frac{π x}{4})

f (x) = 3 x^{2} - 6 x - 24

f (x) = sin (x) 2 x

f (x) = 2 x e^{3 x}

y = x^{4} - x^{3} + 4 x^{2} - 4 x

f (x) = (x - 2)