What is the derivative of 1/2 cos^2(5x) ?

The derivative of 1/2 cos^2(5x) is -(5sin(10x))/2

What is the first derivative of 1/2 cos^2(5x) ?

The first derivative of 1/2 cos^2(5x) is -(5sin(10x))/2

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\frac{d}{d x} (\frac{1}{2} cos^{2} (5 x))

- \frac{5 sin ( 10 x )}{2}

Solution steps

\frac{d}{d x} (\frac{1}{2} cos^{2} (5 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \frac{d}{d x} (cos^{2} (5 x))

Apply the chain rule:

2 cos (5 x) \frac{d}{d x} (cos (5 x))

= 2 cos (5 x) \frac{d}{d x} (cos (5 x))

\frac{d}{d x} (cos (5 x)) = - sin (5 x) \cdot 5

= \frac{1}{2} \cdot 2 cos (5 x) (- sin (5 x) \cdot 5)

Simplify

\frac{1}{2} \cdot 2 cos (5 x) (- sin (5 x) \cdot 5) : - \frac{5 sin ( 10 x )}{2}

= - \frac{5 sin ( 10 x )}{2}

What is the derivative of 1/2 cos^2(5x) ?
The derivative of 1/2 cos^2(5x) is -(5sin(10x))/2
What is the first derivative of 1/2 cos^2(5x) ?
The first derivative of 1/2 cos^2(5x) is -(5sin(10x))/2