Differentiating a logarithmic function in exercise, find the derivative of the function. see examples 1, 2, 3, and 4.
f(x) = 2x ln x

Step-by-step explanation:

From our knowledge of derivatives we use the product rule approach, the product rule is stated below

For f(x)=u(x)v(x) the derivative is express as

hence from the question f(x)=2xlnx,

we can assign u(x)=2x and v(x)=lnx

also the derivative of u(x)=2x is simply

and the derivative of v(x)=lnx can be express using the general log derivative i.e

hence we have

if we substitute value into the general product expression stated earlier we arrive at