Question

derivative of cosx wrt x
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Answer 1

Answer:

-sin(x)

Step-by-step explanation:

There isn't any proof for derivative of cos(x) because by definition derivative of cos(x) w.r.t x is -sin(x), but the below might be an alternative :

sin²x + cos²x = 1

Differentiating on both sides w.r.t x, (via chain rule)

2sin(x)cos(x) + 2cosx[$\frac{d}{dx} cosx$] = 0

Let $\frac{d}{dx} cosx$ = y

⇒ 2sin(x)cos(x) + 2cosx[y] = 0

⇒ 2sin(x)cos(x) = -2cosx[y]

⇒ sin(x) = -y

∴ y = -sin(x)

∴$\frac{d}{dx} cosx$ = -sin(x)

Hoping that I have not made any mistakes, You're welcome.

Hope you have found my answer useful. If my answer deserves a brainliest, do mark it.

GeniusH