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dy dx

dy dx
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You need to find t in terms of x and then you should substitute the expression in terms of x for t in equation `y = ln(1 – t)`  such that:`x = t^3 =gt x^(1/3) = (t^3)^(1/3) =gt root(3) x = t“y = ln(1 – root(3) x)`You need to find `(dy)/(dx), ` hence you need to use chain rule such that:`(dy)/(dx) = ((1 – root(3) x)’)/(1 – root(3) x)“(dy)/(dx) = -((1/3)*x^(1/3 – 1))/(1 – root(3) x)“(dy)/(dx) = -((1/3)*x^(-2/3))/(1 – root(3) x)“(dy)/(dx) = -1/(3*x^(2/3)*(1 – root(3) x))“(dy)/(dx) = -1/(3*root(3)(x^2)*(1 – root(3) x))`Hence, evaluating `(dy)/(dx)`  under given conditions yields `(dy)/(dx) = -1/(3*root(3)(x^2)*(1 – root(3) x)).`
dy dx