1. Derivatives

find the derivative of:
10x^(ln(x))

2. Originally Posted by Asuhuman18
find the derivative of:
10x^(ln(x))
You need to apply the technique called logarithmic differentiation. have you been taught it?

Alternatively, re-write the function as $10 e^{\ln (x^{\ln x})} = 10 e^{\ln (x) \cdot \ln (x)} = 10 e^{[\ln (x)]^2}$ and then apply the chain rule a couple of times.

3. how would you apply chain rule to that function?

4. Originally Posted by Asuhuman18
how would you apply chain rule to that function?
Start by letting $u = [\ln (x)]^2$. Please attempt the calculations before asking for more help. Post what you did and clearly state where you get stuck.

5. [ln(x)]^2
2[ln(x)]*[1/x]=2ln(x)/x. is this right?

6. Originally Posted by Asuhuman18
[ln(x)]^2
2[ln(x)]*[1/x]=2ln(x)/x. is this right?
That is the correct answer for $\frac{du}{dx}$. Now substitute the result into the chain rule formula.