Question

y =log (x^2+2x+5) then dy/dx =?​

Answer 1

AnswEr :

Given,

$\sf \: y = log( {x}^{2} + 2x + 5)y=log(x-2)$

We have to find the derivative of y

Differentiating y with respect to x,

$\longrightarrow \sf \: y' = \dfrac{d \bigg( log( {x}^{2} + 2x + 5) \bigg) }{dx}$

Derivative of log x is 1/x

Using Chain Rule of Differentiation,

$\begin{gathered} \longrightarrow \sf \: y' = \dfrac{1}{ {x}^{2} + 2x + 5} \times \dfrac{d( {x}^{2} + 2x + 5)}{dx} \\ \\ \longrightarrow \boxed{ \boxed{\sf \: y' = \dfrac{2x + 2}{ {x}^{2} + 2x + 5 } }}\end{gathered}$