How do you find the derivative of ${cos}^{4} (2 x)$ $Cos^4(2x)$ ?

Question

How do you find the derivative of ${cos}^{4} (2 x)$ $Cos^4(2x)$ ?

1 Answer

Impact of this question

9844 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-03T14:12:11

Use the chain rule twice.

Explanation:

Recall that we use the notation ${cos}^{4} (u)$ $cos^4 (u)$ to mean ${(cos (u))}^{4}$ $(cos(u))^4$

$\frac{d}{d x} ({(cos (2 x))}^{4}) = 4 {(cos (2 x))}^{3} \frac{d}{d x} (cos (2 x))$ $d/dx( (cos(2x))^4) = 4(cos(2x))^3 d/dx(cos(2x))$

$= 4 {(cos (2 x))}^{3} (- sin (2 x) \frac{d}{d x} (2 x))$ $= 4(cos(2x))^3(-sin(2x) d/dx(2x))$

$= 4 {(cos (2 x))}^{3} (- sin (2 x) (2))$ $= 4(cos(2x))^3(-sin(2x)(2))$

$= - 8 {cos}^{3} (2 x) sin (2 x)$ $= -8cos^3(2x) sin(2x)$

Science

Math

Humanities

... and beyond

How do you find the derivative of ${cos}^{4} (2 x)$ $Cos^4(2x)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the derivative of cos4(2x) Cos^4(2x)?

1 Answer

Explanation:

Related questions

Impact of this question

How do you find the derivative of ${cos}^{4} (2 x)$ $Cos^4(2x)$ ?