# What is the second derivative of?

X^2 • lnX

I have to find the second derivative.

For the first derivative I have: 2x • 1/x

For the second Im stuck at: 2

Any help is much appreciated!

Relevance
• 8 years ago

1/x = x^(-1)

The derivative of that is -x^(-2)

But your first derivative is wrong.

Given f(x) = g(x) * h(x)

f'(x) = g(x) * h'(x) + g'(x) * h(x)

Here, g(x) = x^2

g'(x) = 2x

h(x) = ln(x)

h'(x) = 1/x

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

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

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

f''(x) = 1 + 2 * ln(x) + 2

f''(x) = 3 + 2 * ln(x)

• JoAn
Lv 4
8 years ago

y = x²(ln x)

using product rule

y' = (2x)(ln x) + x²/x

y' = (2x)(ln x) + x

y'' = 2(ln x) + 2x/x + 1

y'' = 2(ln x) + 2 + 1

y'' = 2(ln x) + 3