What is the derivative of #f(x) = e^(x^2 + lnx^3)#?

1 Answer
Steve M
Jun 18, 2018

# f'(x) = e^(x^2+lnx^3) (2x + 3/x)#

Explanation:

We have:

# f(x) = e^(x^2+lnx^3) #

So by the chain rule we have:

# f'(x) = e^(x^2+lnx^3) \ d/dx {x^2+lnx^3}#

# \ \ \ \ \ \ \ \ = e^(x^2+lnx^3) d/dx {x^2 + 3lnx}#

# \ \ \ \ \ \ \ \ = e^(x^2+lnx^3) (2x + 3/x)#

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