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

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

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

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

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

- 5 sin (10 x)

Solution steps

\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

= 2 cos (5 x) (- sin (5 x) \cdot 5)

Simplify

2 cos (5 x) (- sin (5 x) \cdot 5) : - 5 sin (10 x)

= - 5 sin (10 x)

\int (4 cos (x) + 3 x^{3} + 2 sin (x)) d x

\frac{d y}{d x} y^{3} = 5 x^{3} + 2 x

\frac{\partial}{\partial x} (9 + x^{2})

f (x) = 4 x^{2}, at x = 10

\frac{d}{d x} (1500 x + 3000 (2 x + 3)^{- 1} - 1000)

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