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Beliebt Rechnen >

derivative of 7x^4cot(x)

Lösung

\frac{d}{d x} (7 x^{4} cot (x))

Lösung

7 (4 x^{3} cot (x) - x^{4} csc^{2} (x))

Schritte zur Lösung

\frac{d}{d x} (7 x^{4} cot (x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{d}{d x} (x^{4} cot (x))

Wende die Produktregel an:

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

f = x^{4}, g = cot (x)

= 7 (\frac{d}{d x} (x^{4}) cot (x) + \frac{d}{d x} (cot (x)) x^{4})

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

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

= 7 (4 x^{3} cot (x) + (- csc^{2} (x)) x^{4})

Vereinfache

= 7 (4 x^{3} cot (x) - x^{4} csc^{2} (x))

Graph

Beliebte Beispiele

xydx-(1+x^2)dy=0

x y d x - (1 + x^{2}) d y = 0

x^{''}

(dy)/(dx)+3y=40

\frac{d y}{d x} + 3 y = 40

derivative of sqrt(x)(2x+4)

\frac{d}{d x} (x (2 x + 4))

limit as x approaches 7 of (x+6)/(x+1)

x \to 7 lim (\frac{x + 6}{x + 1})