(\partial)/(\partial x)(cos^3(1-5x^2))

Lösung

\frac{\partial}{\partial x} (cos^{3} (1 - 5 x^{2}))

30 x cos^{2} (1 - 5 x^{2}) sin (1 - 5 x^{2})

Schritte zur Lösung

\frac{\partial}{\partial x} (cos^{3} (1 - 5 x^{2}))

Wende die Kettenregel an:

3 (cos (1 - 5 x^{2}))^{2} \frac{\partial}{\partial x} (cos (1 - 5 x^{2}))

= 3 (cos (1 - 5 x^{2}))^{2} \frac{\partial}{\partial x} (cos (1 - 5 x^{2}))

\frac{\partial}{\partial x} (cos (1 - 5 x^{2})) = 10 x sin (1 - 5 x^{2})

= 3 (cos (1 - 5 x^{2}))^{2} \cdot 10 x sin (1 - 5 x^{2})

Vereinfache

= 30 x cos^{2} (1 - 5 x^{2}) sin (1 - 5 x^{2})

\frac{d y}{d x} = 5 y + 1

d er i v a t i v e (\frac{x ^{2} + 8}{x ^{2} - 8})^{3}

\int \frac{1}{36 e ^{- 8 x} + e ^{8 x}} d x

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

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