What is the derivative of-4*sin^2(x+4*sin^2(x+pi/3)) ?

The derivative of-4*sin^2(x+4*sin^2(x+pi/3)) is -6sin(2x)+2sqrt(3)cos(2x)

What is the first derivative of-4*sin^2(x+4*sin^2(x+pi/3)) ?

The first derivative of-4*sin^2(x+4*sin^2(x+pi/3)) is -6sin(2x)+2sqrt(3)cos(2x)

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\frac{d}{d x} (- 4 \cdot sin^{2} (x) + 4 \cdot sin^{2} (x + \frac{π}{3}))

- 6 sin (2 x) + 23 cos (2 x)

Solution steps

\frac{d}{d x} (- 4 sin^{2} (x) + 4 sin^{2} (x + \frac{π}{3}))

Simplify

- 4 sin^{2} (x) + 4 sin^{2} (x + \frac{π}{3}) : 3 cos^{2} (x) - 3 sin^{2} (x) + 3 sin (2 x)

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= - 3 sin (2 x) - 3 sin (2 x) + 3 cos (2 x) \cdot 2

Simplify

= - 6 sin (2 x) + 23 cos (2 x)

What is the derivative of-4*sin^2(x+4*sin^2(x+pi/3)) ?
The derivative of-4*sin^2(x+4*sin^2(x+pi/3)) is -6sin(2x)+2sqrt(3)cos(2x)
What is the first derivative of-4*sin^2(x+4*sin^2(x+pi/3)) ?
The first derivative of-4*sin^2(x+4*sin^2(x+pi/3)) is -6sin(2x)+2sqrt(3)cos(2x)