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Beliebt Rechnen >

derivative of cos^3(4x^2)

Lösung

\frac{d}{d x} (cos^{3} (4 x^{2}))

Lösung

- 24 x cos^{2} (4 x^{2}) sin (4 x^{2})

Schritte zur Lösung

\frac{d}{d x} (cos^{3} (4 x^{2}))

Wende die Kettenregel an:

3 (cos (4 x^{2}))^{2} \frac{d}{d x} (cos (4 x^{2}))

= 3 (cos (4 x^{2}))^{2} \frac{d}{d x} (cos (4 x^{2}))

\frac{d}{d x} (cos (4 x^{2})) = - sin (4 x^{2}) \cdot 8 x

= 3 (cos (4 x^{2}))^{2} (- sin (4 x^{2}) \cdot 8 x)

Vereinfache

= - 24 x cos^{2} (4 x^{2}) sin (4 x^{2})

Graph

Beliebte Beispiele

derivative of ln(ax^n)

\frac{d}{d x} (ln (a x^{n}))

limit as x approaches infinity of 5^{-x}

x \to \infty lim (5^{- x})

derivative (2t)/(4+t^2)

d er i v a t i v e \frac{2 t}{4 + t ^{2}}

limit as x approaches 0 of (5x^3)/(x^3)

x \to 0 lim (\frac{5 x ^{3}}{x ^{3}})

xy^2dy=(x^3+y^3)dx

x y^{2} d y = (x^{3} + y^{3}) d x