Question
Y=³√3×-4 using differentiation to solve
Answers
GPT 3.5
To find the derivative of Y = ³√(3x - 4), we can first rewrite the function using the power rule for differentiation for radicals:
Y = (3x - 4)^(1/3)
Now we can apply the chain rule of differentiation to find the derivative.
Let u = 3x - 4, then Y = u^(1/3)
Now find the derivative of Y with respect to x:
Y' = (1/3) * u^(-2/3) * u'
Y' = (1/3) * (3x - 4)^(-2/3) * 3
Y' = (1/3) * 3 / (3x - 4)^(2/3)
Y' = 1 / (3x - 4)^(2/3)
So the derivative of Y = ³√(3x - 4) is Y' = 1 / (3x - 4)^(2/3).
Y = (3x - 4)^(1/3)
Now we can apply the chain rule of differentiation to find the derivative.
Let u = 3x - 4, then Y = u^(1/3)
Now find the derivative of Y with respect to x:
Y' = (1/3) * u^(-2/3) * u'
Y' = (1/3) * (3x - 4)^(-2/3) * 3
Y' = (1/3) * 3 / (3x - 4)^(2/3)
Y' = 1 / (3x - 4)^(2/3)
So the derivative of Y = ³√(3x - 4) is Y' = 1 / (3x - 4)^(2/3).