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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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