What is the derivative of sin^5(x/3) ?

The derivative of sin^5(x/3) is 5/3 sin^4(x/3)cos(x/3)

What is the first derivative of sin^5(x/3) ?

The first derivative of sin^5(x/3) is 5/3 sin^4(x/3)cos(x/3)

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\frac{d}{d x} (sin^{5} (\frac{x}{3}))

\frac{5}{3} sin^{4} (\frac{x}{3}) cos (\frac{x}{3})

Solution steps

\frac{d}{d x} (sin^{5} (\frac{x}{3}))

Apply the chain rule:

5 (sin (\frac{x}{3}))^{4} \frac{d}{d x} (sin (\frac{x}{3}))

= 5 (sin (\frac{x}{3}))^{4} \frac{d}{d x} (sin (\frac{x}{3}))

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

= 5 (sin (\frac{x}{3}))^{4} cos (\frac{x}{3}) \frac{1}{3}

Simplify

5 sin^{4} (\frac{x}{3}) cos (\frac{x}{3}) \frac{1}{3} : \frac{5}{3} sin^{4} (\frac{x}{3}) cos (\frac{x}{3})

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

\int \frac{1}{x ^{2} 8 - x ^{2}} d x

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

\int \frac{x}{x + 3} d x

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

t \to 3 lim (2 t^{- 1})

What is the derivative of sin^5(x/3) ?
The derivative of sin^5(x/3) is 5/3 sin^4(x/3)cos(x/3)
What is the first derivative of sin^5(x/3) ?
The first derivative of sin^5(x/3) is 5/3 sin^4(x/3)cos(x/3)