Derivative of products of two functions

Question

I have a function $V$ which is a product of two functions: $$V = λ(x_1^α+x_2^α).$$ How would I be able to differentiate it with respect to $λ$ and $α$, i.e., $$\frac{∂V}{∂λ},\ \frac{∂V}{∂α}?$$ Thanks.

Answer 1

That's easy. $$\frac{\partial V}{\partial\lambda}=x_1^\alpha+x_2^\alpha$$ and $$\frac{\partial V}{\partial\alpha}=\lambda(x_1^\alpha \ln x_1+x_2^\alpha \ln x_2)$$