What is the derivative of 3sin(x-4sin^3(x)) ?

The derivative of 3sin(x-4sin^3(x)) is 3cos(x)-12sin^2(x)cos(x)

What is the first derivative of 3sin(x-4sin^3(x)) ?

The first derivative of 3sin(x-4sin^3(x)) is 3cos(x)-12sin^2(x)cos(x)

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

3 cos (x) - 12 sin^{2} (x) cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (4 sin^{3} (x)) = 12 sin^{2} (x) cos (x)

= 3 cos (x) - 12 sin^{2} (x) cos (x)

What is the derivative of 3sin(x-4sin^3(x)) ?
The derivative of 3sin(x-4sin^3(x)) is 3cos(x)-12sin^2(x)cos(x)
What is the first derivative of 3sin(x-4sin^3(x)) ?
The first derivative of 3sin(x-4sin^3(x)) is 3cos(x)-12sin^2(x)cos(x)