Differentiation wrt to L

Question

I need to differentiate a equation which I have some problem with.

The equation looks like this:

$(K-L)(x/L)^{\gamma}$.

I need to differentiate this wrt to L. Not able to do it.

Need some guidance on this.

Answer 1

Let $F(L) = (K-L)( \frac{x}{L} )^{\gamma} = K(\frac{x}{L})^\gamma - \frac{x^\gamma}{L^{\gamma - 1}}$

$$\therefore \frac{dF}{dL} = - \gamma K x^{\gamma} L^{-\gamma - 1} - (1 - \gamma)x^\gamma L^{-\gamma}$$

Answer 2

$-(x/L)^\gamma+(K-L)(-\gamma)x^\gamma L^{-\gamma-1}$

Answer 3

Derivative of $F(L)=(K-L)(x/L)^{\gamma}$ is \begin{equation} F'(L)=\gamma(-K+L)\frac{x^{\gamma}}{L^{\gamma+1}}-(x/L)^{\gamma} \end{equation} using the chain and product rule. I can't see any equation in the question though...