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Beliebt Rechnen >

derivative f(x)=6x^3cot(x)

Lösung

ableitung von

f (x) = 6 x^{3} cot (x)

Lösung

6 (3 x^{2} cot (x) - x^{3} csc^{2} (x))

Schritte zur Lösung

\frac{d}{d x} (6 x^{3} cot (x))

Entferne die Konstante:

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

= 6 \frac{d}{d x} (x^{3} cot (x))

Wende die Produktregel an:

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

f = x^{3}, g = cot (x)

= 6 (\frac{d}{d x} (x^{3}) cot (x) + \frac{d}{d x} (cot (x)) x^{3})

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

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

= 6 (3 x^{2} cot (x) + (- csc^{2} (x)) x^{3})

Vereinfache

= 6 (3 x^{2} cot (x) - x^{3} csc^{2} (x))

Graph

Beliebte Beispiele

tangent f(x)=x^3sqrt(5-x^2),\at x=2

t an g e n t f (x) = x^{3} 5 - x^{2}, at x = 2

derivative of-1/2 e^{-x^2}

\frac{d}{d x} (- \frac{1}{2} e^{- x^{2}})

(\partial)/(\partial x)(sqrt(x^3+sin(3y)))

\frac{\partial}{\partial x} (x^{3} + sin (3 y))

integral of 1/(sqrt(x^2+c))

\int \frac{1}{x ^{2} + c} d x

inverselaplace 2/((s-4)^3)

in v erse l a pl a ce \frac{2}{( s - 4 ) ^{3}}