Question

Differentiate y = x In (x)

Post relevant answers.....
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Answer 1

Answer:

we take natural logs of both sides and simplify:

ln(x

y

)=ln(y

x

)→yln(x)=xln(y)

use implicit differentiation, taking derivatives of both sides with respect to x:

y′ln(x)+y⋅

x

1

=1⋅ln(y)+x⋅

y

y′

Solving for y

′

y′ln(x)−

y

xy′

=ln(y)−

x

y

Implies that:

y′=

ln(x)−

y

x

ln(y)−

x

y

=

xyln(x)−x

2

xyln(y)−y

2

Explanation:

Hope this helps mate.