Question

Differentiate The Function. If Possible, First Use Properties Of Logarithms To Simplify The Given Function. Y=(X2+3)Ln(X2+3) Y′=

Answer 1

To differentiate the function Y=(X^2+3)Ln(X^2+3), we can simplify the function using the properties of logarithms. The derivative of Y is 1 + ln(X^2+3) + 2X.

Step-by-step explanation:

To differentiate the function Y=(X2+3)Ln(X2+3), we can simplify the function using the properties of logarithms. The given function can be simplified as Y=(X2+3)ln(X2+3), where ln represents the natural logarithm. We can differentiate this function using the product rule and the chain rule.

1. 
   
3. First, let's simplify the function by applying the properties of logarithms. We have Y=(X2+3)ln(X2+3).
4. 
   
6. Next, let's differentiate the function using the product rule: y' = (X2+3) * (d/dx(ln(X2+3))) + ln(X2+3) * (d/dx(X2+3)).
7. 
   
9. To find the derivative of ln(X2+3), we use the chain rule: d/dx(ln(X2+3)) = 1/(X2+3) * d/dx(X2+3).
10. 
    
12. Substituting this back into the equation, we have y' = (X2+3) * (1/(X2+3) * d/dx(X2+3)) + ln(X2+3) * (d/dx(X2+3)).
13. 
    
15. Simplifying further, we get y' = 1 + ln(X2+3) + 2X.

Learn more about Differentiating a logarithmic function