Question

Find the derivative with respect to x of y = (3x + x^2)^5

Answer 1

The required "option A)
`5(3x + x^2)^(4) (3+2x)`" is correct.

Explanation:

We have,

`y = (3x + x^2)^5` ..... (1)

To find,
`(dy)/(dx)` = ?

Differentiating equation (1) w.r.t. 'x', we get

`(dy)/(dx)= (d[(3x + x^2)^5])/(dx)`

⇒
`(dy)/(dx)=5(3x + x^2)^(5-1) (d(3x + x^2))/(dx)`

[ ∵
`y=x^(n)` ⇒
`(dy)/(dx)=nx^(n-1)`]

⇒
`(dy)/(dx)=5(3x + x^2)^(4) (3(1) + 2x^(2-1))`

⇒
`(dy)/(dx)=5(3x + x^2)^(4) (3+2x)`

Thus, the required "option A)
`5(3x + x^2)^(4) (3+2x)`" is correct.