# f(x)Differentiate f(x)=2x^2 * ln x

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We have the function f(x) = 2x^2 * ln x to differentiate.

Use the product rule:

f'(x) = (2x^2)' * ln x + 2x^2 * (ln x)'

f'(x) = 4x*ln x + 2x^2*(1/x)

f'(x) = 4x*ln x + 2x

**The derivative of 2x^2 * ln x is 2x(ln (x^2) + 1)**

We'll calculate the first derivative of f(x).

We'll put f(x) = y

We'll differentiate with respect to x:

dy/dx =(d/dx) (2x^2 * ln x)

dy/dx =[(d/dx) (2x^2)] * ln x + 2x^2*(d/dx)ln x)

dy/dx = 4xlnx + 2x^2/x

We'll simplify and we'll get:

dy/dx = 4xlnx + 2x

We'll factorize by 2x:

dy/dx = 2x(2lnx + 1)

dy/dx = 2x(ln x^2 + lne)

**dy/dx = 2x ln(e*x^2)**