How to distribute this?

Question

1st: Q = 10(L,K) ^0.5

The book says: that the partial derivitve equals:

5 K/L with respect to L and 5 L/K with respect to K.

But how do they come up with 5?

Answer 1

Probably the question is to find partial derivatives of the expression:

Q = 10*(L*K)^0.5 = 10*sqrt(L*K)

In this case dQ/dL = 5*sqrt(K/L) and dQ/dK = 5*sqrt(L/K), where sqrt(x) = x^0.5 is square root of x.

Answer 2

0.5 x 10 = 5

Answer 3

when you derive, you pull down the .5...so it is 10*.5=5 is how they come up with the five.;

Answer 4

0.5*10=5

Answer 5

I don't think you mean "distribute" here. that's like a(b+c) = ab + bc. taking the derivative, even a partial derivative, you use the "power rule". ie, df/dx of x^2 is 2x. another, df/dx of 4x^3 is 12x^2. so dQ/dL is (0.5)(10)Q^(0.5-1) = 5Q^(-0.5)

Answer 6

Question not clear