Question

differentiate the following​

Answer 1

Answer:

d/dx=(x2+5x+6)1/2

dy/dx =1/2(x2+5x+6)-1/2(2x+5)

dy/dx=(2x+5)/2(x2+5x+6)1/2

Answer 2

Answer:

$f'(x) = \frac{2x+5}{2\sqrt{(x^2+5x+6)} }$

Step-by-step explanation:

Given:

f(x) = $\sqrt{x^2+5x+6}$

To find:

f'(x)

Solution:

$f(x) = \sqrt{x^2+5x+6}$

$f'(x) = \frac{1}{2\sqrt{x^2+5x+6} } * 2x +5$

$f'(x) = \frac{2x+5}{2\sqrt{(x^2+5x+6)} }$

Hence the derivative of $\sqrt{x^2+5x+6}$ is  $\frac{2x+5}{2\sqrt{(x^2+5x+6)} }$