Question

find d/dx when y=log e(x^3)​

Answer 1

y = loge(x^3)

y = ln(x^3)

Let x^3 = u

Differentiate with respect to x,

3x^2 = du/dx .......................... (i)

Now,

y = ln(x^3)

y = ln(u)

Differentiate with respect to u,

dy/du = 1/u

dy/du = 1/x^3 .........................(ii)

Multiply (i) and (ii),

dy/du × du/dx = 1/x^3 × 3x^2

=> dy/dx = 3/x

Hence, dy/dx when y = ln(x^3) is: 3/x

That is, dy/dx = 3/x