1. ## Derivatives problems

Find an equation of the tangent line to the curve at the point (1, 1).

y = ln (xe^x^4)

in order to find the slope i take the derivative so i use product and chain rule, it become (1/xe^x^4)(1(ex)^4+4x(ex )^3(ex)) and i know once i get the slope i can just use y-y1=m(x-x1) but somehow the slope is not right? is it the step i take the derivative wrong?

2. I'm assuming this is it : $y = \ln \left(xe^{x^4}\right)$

If it is so, then you should be careful with your exponents. $e^{x^4} \neq \left(e^x\right)^4$

So when differentiating $e^{x^4}$, it should be: $e^{x^4} \cdot \left(x^4\right)' = e^{x^4} \cdot 4x^3$

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As an alternative, you can make your life easier by using some logarithmic properties first before differentiating:
$y = \ln \left(xe^{x^4}\right) = \ln x + \ln e^{x^4} = \ln x + x^4$