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

The derivative of (sin(3x)^3+5x) is 9sin^2(3x)cos(3x)+5

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

The first derivative of (sin(3x)^3+5x) is 9sin^2(3x)cos(3x)+5

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

9 sin^{2} (3 x) cos (3 x) + 5

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} ((sin (3 x))^{3}) = 9 sin^{2} (3 x) cos (3 x)

\frac{d}{d x} (5 x) = 5

= 9 sin^{2} (3 x) cos (3 x) + 5

What is the derivative of (sin(3x)^3+5x) ?
The derivative of (sin(3x)^3+5x) is 9sin^2(3x)cos(3x)+5
What is the first derivative of (sin(3x)^3+5x) ?
The first derivative of (sin(3x)^3+5x) is 9sin^2(3x)cos(3x)+5