What is the derivative of cos^3(x/3) ?

The derivative of cos^3(x/3) is -cos^2(x/3)sin(x/3)

What is the first derivative of cos^3(x/3) ?

The first derivative of cos^3(x/3) is -cos^2(x/3)sin(x/3)

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

- cos^{2} (\frac{x}{3}) sin (\frac{x}{3})

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (cos (\frac{x}{3})) = - sin (\frac{x}{3}) \frac{1}{3}

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

Simplify

3 cos^{2} (\frac{x}{3}) (- sin (\frac{x}{3}) \frac{1}{3}) : - cos^{2} (\frac{x}{3}) sin (\frac{x}{3})

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

y^{^{''}} - 4 y^{^{'}} + 21 y = 0

\int (x^{2} + sin (x)) d x

\frac{d}{d x} (a^{2} - x^{2})

y = 5 x + 2

k = 3 \sum \infty \frac{3}{k ^{2} - 2 k}

What is the derivative of cos^3(x/3) ?
The derivative of cos^3(x/3) is -cos^2(x/3)sin(x/3)
What is the first derivative of cos^3(x/3) ?
The first derivative of cos^3(x/3) is -cos^2(x/3)sin(x/3)