Find y' and y''. y = sqrt(x) * ln(x)

Question

calculus, derivatives with natural logs

 

Answer 1

Rewrite the function using rational exponents.

 

y = x^1/2lnx

 

 

Use the product and logarithmic differentiation.

 

y' = (1/2)x^-1/2lnx + x^1/2x^-1

y' = (1/2)x^1/2lnx + x^-1/2

 

 

Then to find y'', take the derivative of y'.