Question

find
dy/dx if y = cos(x^5 – 1)​

Answer 1

Answer:

y = cos ⁵ ( x )

Differentiate using the chain rule , which states that d / DX [ f ( g ( x ) ) is f ' ( g ( x ) ) g ' ( x ) where f ( x ) = x ⁵ and g ( x ) = cos ( x ) .

To apply the chain Rule ,set u as cos ( x ) .

d / du [ u ⁵ ] d / dx [ cos ( x ) ]

Differentiate using the power role which states that d / du [ un ] is nu n -¹ where n = 5 .

5 u ⁴ d / DX [ cos ( x ) ]

Replace all occurance of u with cos ( x ) .

5 cos ⁴ ( x ) d ) DX [ cos ( x ) ]

The derivation of cos ( x ) with respect to x is - sin ( x )

5 cos ⁴ ( x ) ( - sin ( x ) )

Multiple - 1 by 5

- 5 cos ⁴ ( x ) sin ( x )

Answer 2

Step-by-step explanation:

y = cos(x^5 – 1)

differentiating,

dy/dx=d{cos(x^5 – 1)}/dx

= {-sin(x^5-1)}{5x^4}