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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

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}

y^{^{''}} - 2 y^{^{'}} = 12 x - 10

3 x^{2} + 2 x

x^{2} - 4, 5

\int_{1}^{2} x^{3} + \frac{1}{4 x ^{3}} d x

x \to \infty lim (- 7)

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