What is the derivative of cos^2(5x^2+6x+5) ?

The derivative of cos^2(5x^2+6x+5) is -sin(2(5+5x^2+6x))(6+10x)

What is the first derivative of cos^2(5x^2+6x+5) ?

The first derivative of cos^2(5x^2+6x+5) is -sin(2(5+5x^2+6x))(6+10x)

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derivative of

cos^{2} (5 x^{2} + 6 x + 5)

- sin (2 (5 + 5 x^{2} + 6 x)) (6 + 10 x)

Solution steps

\frac{d}{d x} (cos^{2} (5 x^{2} + 6 x + 5))

Apply the chain rule:

2 cos (5 x^{2} + 6 x + 5) \frac{d}{d x} (cos (5 x^{2} + 6 x + 5))

= 2 cos (5 x^{2} + 6 x + 5) \frac{d}{d x} (cos (5 x^{2} + 6 x + 5))

\frac{d}{d x} (cos (5 x^{2} + 6 x + 5)) = - sin (5 x^{2} + 6 x + 5) (10 x + 6)

= 2 cos (5 x^{2} + 6 x + 5) (- sin (5 x^{2} + 6 x + 5) (10 x + 6))

Simplify

2 cos (5 x^{2} + 6 x + 5) (- sin (5 x^{2} + 6 x + 5) (10 x + 6)) : - sin (2 (5 + 5 x^{2} + 6 x)) (6 + 10 x)

= - sin (2 (5 + 5 x^{2} + 6 x)) (6 + 10 x)

What is the derivative of cos^2(5x^2+6x+5) ?
The derivative of cos^2(5x^2+6x+5) is -sin(2(5+5x^2+6x))(6+10x)
What is the first derivative of cos^2(5x^2+6x+5) ?
The first derivative of cos^2(5x^2+6x+5) is -sin(2(5+5x^2+6x))(6+10x)