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Beliebt Rechnen >

derivative f(x)=-3x^5cos(x)

Lösung

ableitung von

f (x) = - 3 x^{5} cos (x)

Lösung

- 3 (5 x^{4} cos (x) - x^{5} sin (x))

Schritte zur Lösung

\frac{d}{d x} (- 3 x^{5} cos (x))

Entferne die Konstante:

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

= - 3 \frac{d}{d x} (x^{5} cos (x))

Wende die Produktregel an:

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

f = x^{5}, g = cos (x)

= - 3 (\frac{d}{d x} (x^{5}) cos (x) + \frac{d}{d x} (cos (x)) x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (cos (x)) = - sin (x)

= - 3 (5 x^{4} cos (x) + (- sin (x)) x^{5})

Vereinfache

= - 3 (5 x^{4} cos (x) - x^{5} sin (x))

Graph

Beliebte Beispiele

integral of (x^3)/((1+x^4)^{1/2)}

\int \frac{x ^{3}}{( 1 + x ^{4} ) ^{\frac{1}{2}}} d x

derivative f(x)=x^{5/2}e^x

d er i v a t i v e f (x) = x^{\frac{5}{2}} e^{x}

integral of sec^2(x)csc(x)

\int sec^{2} (x) csc (x) d x

integral of 3sin^2(x)cos(x)

\int 3 sin^{2} (x) cos (x) d x

inverselaplace 6/((s-2)^4*(s+2)^2)

in v erse l a pl a ce \frac{6}{( s - 2 ) ^{4} \cdot ( s + 2 ) ^{2}}