What is the derivative of sin^3(2x+x^2) ?

The derivative of sin^3(2x+x^2) is 6sin^2(2x)cos(2x)+2x

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

The first derivative of sin^3(2x+x^2) is 6sin^2(2x)cos(2x)+2x

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

6 sin^{2} (2 x) cos (2 x) + 2 x

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (sin^{3} (2 x)) = 6 sin^{2} (2 x) cos (2 x)

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

= 6 sin^{2} (2 x) cos (2 x) + 2 x

What is the derivative of sin^3(2x+x^2) ?
The derivative of sin^3(2x+x^2) is 6sin^2(2x)cos(2x)+2x
What is the first derivative of sin^3(2x+x^2) ?
The first derivative of sin^3(2x+x^2) is 6sin^2(2x)cos(2x)+2x