derive x2ln(3x^2+5x)
product rule
Let f(x) = x^2 and g(x) = ln(3x^2 + 5x)
Using the product rule, we have:
(fg)' = f'g + fg'
Now, let's find the derivatives:
f'(x) = 2x
g'(x) = (1 / (3x^2 + 5x)) * (6x + 5)
Now, we can calculate the derivative of x^2ln(3x^2 + 5x) using the product rule:
(x^2ln(3x^2 + 5x))' = (2x)(ln(3x^2 + 5x)) + (x^2)(1 / (3x^2 + 5x))(6x + 5)
Simplifying further:
= 2xln(3x^2 + 5x) + 6x + 5x
= 2xln(3x^2 + 5x) + 11x
Therefore, the derivative of x^2ln(3x^2 + 5x) is 2xln(3x^2 + 5x) + 11x.