Question

In Exercise, find the derivative of the function.
y = ln(3 + x2)

Answer 1

Answer:
`(2x)/(3 + x^2)`

Explanation:

We know the property of derivative:
`(d)/(dx)(\log (x))=(1)/(x)`

Given function :
`y=\ln(3 + x^2)`

Differentiate both sides with respect to x , we get

`(dy)/(dx)=(d)/(dx)(\ln(3 + x^2))`

`\Rightarrow\ (dy)/(dx)=(1)/(3 + x^2)\cdot(d)/(dx)(3 + x^2)` [By Chain rule]

`\Rightarrow\ (dy)/(dx)=(1)/(3 + x^2)\cdot(0+2x)`

[Since
`(d)/(dx)(a)=0` , where a is scalar and
`(d)/(dx)(x^n)=n(x)^(n-1)`]

`\Rightarrow\ (dy)/(dx)=(2x)/(3 + x^2)`

Hence, the derivative of the given function is
`(2x)/(3 + x^2)` .