What is the derivative of sin(x-1/3 sin^3(x)) ?

The derivative of sin(x-1/3 sin^3(x)) is cos^3(x)

What is the first derivative of sin(x-1/3 sin^3(x)) ?

The first derivative of sin(x-1/3 sin^3(x)) is cos^3(x)

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

cos^{3} (x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Rewrite using trig identities

= cos^{3} (x)

\int - 25 sin (5 t - \frac{π}{2}) d t

y^{^{'}} + x e^{y} = 0

\int e^{x} 5 + e^{x} d x

f (x) = 3 x sin (x)

f (x) = \frac{8 x ^{3} - 2 x + 9}{x}

What is the derivative of sin(x-1/3 sin^3(x)) ?
The derivative of sin(x-1/3 sin^3(x)) is cos^3(x)
What is the first derivative of sin(x-1/3 sin^3(x)) ?
The first derivative of sin(x-1/3 sin^3(x)) is cos^3(x)