Use a rule to differentiate u = ⁵√t + 4√t⁵?
Could you use product rule for this? If so how do you do it..
Also could you use the exponent rule? and how do you know when to use the exponent rule or the product rule..?
Thanks!
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u = t^(1/5) + 4 (t^5)^(1/2) = t^(1/5) + 4 t^(5/2)
du/dt = (1/5) t^(1/5 - 1) + 4 (5/2) t^(5/2 - 1) = 1/5 t^(-4/5) + 10 t^(3/2)
u = ⁵√t + 4√t⁵
u = t ⁵/² + 4 t⁵
u = t ^2.5 + 4 t⁵
u' = 2.5 t ^ 1.5 + 20 t ^ 4
u = ⁵√t + 4√t⁵ = (t)^(1/5) + [t^5]^1/4 = t^(1/5) + t^(5/4)
du/dt = 1/5t^(1/5-1) + 5/4t^(5/4-1) = 1/5t^(-4/5) + 5/4t^(1/5) = 1/5t^(4/5) + 5/4t^(1/5)