Question

differentiate the following functions w.r.t x . (i)(x^3-2x-1)^5​

Answer 1

Answer:

( 15 x² - 10 ) . ( x³ - 2 x - 1 )⁴

Step-by-step explanation:

Given :

f ( x ) = ( x³ - 2 x - 1 )⁵

We are asked to find f' ( x ) or y' :

Diff. w.r.t. x :

y' = 5 ( x³ - 2 x - 1 )⁵⁻¹ . ( x³ - 2 x - 1 )'

y' = 5 ( x³ - 2 x - 1 )⁴ . ( x³ - 2 x - 1 )'

y' = 5 ( x³ - 2 x - 1 )⁴ . ( 3 x³⁻¹ - 2 x¹⁻¹ - 0 )

y' = 5 ( x³ - 2 x - 1 )⁴ . ( 3 x²- 2 x¹⁻¹ - 0 )

y' = 5 ( x³ - 2 x - 1 )⁴ . ( 3 x²- 2 x⁰- 0 )

y' = 5 ( x³ - 2 x - 1 )⁴ . ( 3 x²- 2 - 0 )

y' = 5 ( x³ - 2 x - 1 )⁴ . ( 3 x²- 2  )

y' =  ( 15 x² - 10 ) . ( x³ - 2 x - 1 )⁴

Hence we get required answer!