What is the derivative of 4cos^2(x-4cos(x)+1) ?

The derivative of 4cos^2(x-4cos(x)+1) is 4sin(x)-4sin(2x)

What is the first derivative of 4cos^2(x-4cos(x)+1) ?

The first derivative of 4cos^2(x-4cos(x)+1) is 4sin(x)-4sin(2x)

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\frac{d}{d x} (4 cos^{2} (x) - 4 cos (x) + 1)

4 sin (x) - 4 sin (2 x)

Solution steps

\frac{d}{d x} (4 cos^{2} (x) - 4 cos (x) + 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 cos^{2} (x)) - \frac{d}{d x} (4 cos (x)) + \frac{d}{d x} (1)

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

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

\frac{d}{d x} (1) = 0

= - 4 sin (2 x) - (- 4 sin (x)) + 0

Simplify

= 4 sin (x) - 4 sin (2 x)

y = x + \frac{1}{2}

y = \frac{ln ( x ^{2} )}{x}

f (x) = arccot (2 x)

f (x) = 6 sin (x) tan (x) + 6 cos (x)

f (x) = {x ln ∣ 4 x ∣ : x \neq = 0, 1 : x = 0}

What is the derivative of 4cos^2(x-4cos(x)+1) ?
The derivative of 4cos^2(x-4cos(x)+1) is 4sin(x)-4sin(2x)
What is the first derivative of 4cos^2(x-4cos(x)+1) ?
The first derivative of 4cos^2(x-4cos(x)+1) is 4sin(x)-4sin(2x)