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

The derivative of (-cos(4x+1)^2+1) is 8sin(4x)-4sin(8x)

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

The first derivative of (-cos(4x+1)^2+1) is 8sin(4x)-4sin(8x)

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

8 sin (4 x) - 4 sin (8 x)

Solution steps

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

Simplify

(- cos (4 x) + 1)^{2} + 1 : cos^{2} (4 x) - 2 cos (4 x) + 2

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (cos^{2} (4 x)) = - 4 sin (8 x)

\frac{d}{d x} (2 cos (4 x)) = - 8 sin (4 x)

\frac{d}{d x} (2) = 0

= - 4 sin (8 x) - (- 8 sin (4 x)) + 0

Simplify

= 8 sin (4 x) - 4 sin (8 x)

y = - x^{2} + 4, y = 3 x

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

\frac{d y}{d x} = 6 y e^{x + 9}

x \to 0 lim ((1 - \frac{1}{x})^{x})

\int_{80}^{90} \frac{x - 80}{800} d x

What is the derivative of (-cos(4x+1)^2+1) ?
The derivative of (-cos(4x+1)^2+1) is 8sin(4x)-4sin(8x)
What is the first derivative of (-cos(4x+1)^2+1) ?
The first derivative of (-cos(4x+1)^2+1) is 8sin(4x)-4sin(8x)