derivative of cos^4(3x^2)

Lösung

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

- 24 x cos^{3} (3 x^{2}) sin (3 x^{2})

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (cos (3 x^{2})) = - sin (3 x^{2}) \cdot 6 x

= 4 (cos (3 x^{2}))^{3} (- sin (3 x^{2}) \cdot 6 x)

Vereinfache

= - 24 x cos^{3} (3 x^{2}) sin (3 x^{2})

\int_{- 1}^{- 2} \frac{16 - x ^{3}}{x ^{3}} d x

\int 5 sin^{3} (5 x) cos^{3} (5 x) d x

\frac{\partial}{\partial x} (x^{2} y + e^{x y})

\int_{0}^{4.5} 90 x d x

\frac{d}{d x} (1 + 2 tan (x))