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Beliebt Rechnen >

derivative ((cos(x)))/(cos^2(*x)-1)

Lösung

ableitung von

\frac{( cos ( x ) )}{cos ^{2} ( \cdot x ) - 1}

Lösung

- csc (x) + 2 csc^{3} (x)

Schritte zur Lösung

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

Vereinfache

\frac{cos ( x )}{cos ^{2} ( x ) - 1} : - cot (x) csc (x)

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = cot (x), g = csc (x)

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of (n+3)3

\int (n + 3) 3 d n

integral of 2/(e^x+2)

\int \frac{2}{e ^{x} + 2} d x

tangent f(x)=(36x)/(x^2+36),\at x=-3

t an g e n t f (x) = \frac{36 x}{x ^{2} + 36}, at x = - 3

integral of x/((1+x)^3)

\int \frac{x}{( 1 + x ) ^{3}} d x

(\partial)/(\partial x)(e^{3x}cos(4x))

\frac{\partial}{\partial x} (e^{3 x} cos (4 x))