Question

Find, yʹ if y=ln(1+x⁴) eˣ²; yʹ=2 x[2 x²/1+x⁴+ln(1+x⁴)] eˣ² ]

Answer 1

To find y', use the product rule and chain rule to differentiate y = ln(1+x⁴) eˣ² with respect to x.

Step-by-step explanation:

To find y', we need to differentiate y with respect to x. y = ln(1+x⁴) eˣ²

To do this, we can use the product rule and chain rule:

1. Let u = ln(1+x⁴) and v = eˣ²
2. Find du/dx by differentiating u with respect to x
3. Find dv/dx by differentiating v with respect to x
4. Then, y' = u'v + uv'
5. Substitute the values of u, v, du/dx, and dv/dx into the equation to find y'