Question

differentiate (solve)
y=cube root3x-4

Answer 1

To differentiate the function y = cuberoot(3x - 4), we need to use the chain rule for differentiation as follows:

y = (3x - 4)^(1/3)

Let u = 3x - 4, then y = u^(1/3).

Now, we can apply the chain rule:

dy/dx = (1/3)u^(-2/3)(du/dx)

Substitute u = 3x - 4 back in:

dy/dx = (1/3)(3x - 4)^(-2/3)(d/dx(3x - 4))

dy/dx = (1/3)(3x - 4)^(-2/3)(3)

dy/dx = 1/(3(3x - 4)^(2/3))

Therefore, the derivative of y = cuberoot(3x - 4) is dy/dx = 1/(3(3x - 4)^(2/3)).