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If y=(1)/(4)u^(4),u=(2)/(3)x^(3)+5, the...

If `y=(1)/(4)u^(4),u=(2)/(3)x^(3)+5`, then `(dy)/(dx)=`

A

`(1)/(27) x^(2) (2x^(3) + 15)^(3) `

B

`(2)/(27) x (2x^(3) + 5)^(3) `

C

`(2)/(27) x^(2) (2x^(3) + 15)^(3) `

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(dy)/(dx) = (1)/(4) .4u^(3) = u^(3) " and " (du)/(dx) = (2)/(3) . 3x^(2) = 2x^(2) `
` therefore (dy)/(dx) = (dy)/(du)(du)/(dx) = u^(3) . 2x^(2)`
`= ((2)/(3) x^(3) + 5)^(3) . 2x^(2)`
` = ((2x^(3) + 15)^(3))/(27) . 2x^(2)`
` (2)/(27) x^(2)(2x^(3) + 15)^(3)` .
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