Question

dy/dx=d/dx[cos(sinx)]​

Answer 1

ANSWER:

dy/dx = -cos x [sin (sin x) ]

GIVEN:

dy/dx = d/dx [cos(sin x)]

TO FIND:

dy/dx = ??

FORMULAE:

d/dx (Cos x) = - Sin x

d/dx (Sin x) = Cos x

(dx/dx) = 1

EXPLANATION:

dy/dx = d/dx [cos(sin x)]

dy/dx = -sin (sin x) × d/dx (sin x)

dy/dx = -sin (sin x) × cos x × (dx/dx)

dy/dx = -cos x [sin (sin x) ]

EXTRA FORMULAE:

• d/dx (Constant) = 0

• d/dx (tan x) = sec² x

• d/dx ( sec x) = sec x tan x

• d/dx (cosec x) = - cosec x cot x

• d/dx (cot x) = - cosec² x

Answer 2

Answer:

Step-by-step explanation:

d/dx[cos(sin(x)]

Assuming sin(x) = u,

d/dx(cos(u))

⇒ -sin(u) · du/dx

⇒ -sin[sin(x)] · d/dx(sin(x))

⇒ -sin[sin(x)] · cos(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