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Beliebt Rechnen >

derivative 9x^2cos(x)cot(x)

Lösung

ableitung von

9 x^{2} cos (x) cot (x)

Lösung

9 (2 x cos (x) cot (x) + (- cos (x) - cot (x) csc (x)) x^{2})

Schritte zur Lösung

\frac{d}{d x} (9 x^{2} cos (x) cot (x))

Entferne die Konstante:

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

= 9 \frac{d}{d x} (x^{2} cos (x) cot (x))

Wende die Produktregel an:

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

f = x^{2}, g = cos (x) cot (x)

= 9 (\frac{d}{d x} (x^{2}) cos (x) cot (x) + \frac{d}{d x} (cos (x) cot (x)) x^{2})

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

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

= 9 (2 x cos (x) cot (x) + (- cos (x) - cot (x) csc (x)) x^{2})

Graph

Beliebte Beispiele

tangent f(x)= 7/(sqrt(x)),(4, 7/2)

t an g e n t f (x) = \frac{7}{x}, (4, \frac{7}{2})

(dy)/(dx)-2y=e^{5x}

\frac{d y}{d x} - 2 y = e^{5 x}

derivative of-5sin(2x)

\frac{d}{d x} (- 5 sin (2 x))

derivative of cos(x+1)

\frac{d}{d x} (cos (x + 1))

x^2y^{''}-4xy^'-36y=0

x^{2} y^{^{''}} - 4 x y^{^{'}} - 36 y = 0