find the derivative with respect to x:

sqrt(x+s) = (1/x) + (1/s)

Find the derivative of what?

of the equation that i put...

sqrt(x+s)=(1/x)+(1/s)

you have to take the derivative of both sides but i'm getting stuck

1/2 * 1 /sqrt(x+s)=-1/x^2 This assumes s is a constant.

To find the derivative of the given equation with respect to x, we can apply the power rule and the chain rule.

Let's break down the given equation step by step:

sqrt(x + s) = (1/x) + (1/s)

Step 1: Rewrite the equation
(x + s)^(1/2) = 1/x + 1/s

Step 2: Take the derivative of both sides with respect to x
d/dx [(x + s)^(1/2)] = d/dx (1/x) + d/dx (1/s)

Step 3: Apply the power rule
(1/2)(x + s)^(-1/2) = -1/x^2

Step 4: Simplify the right-hand side
(1/2)(x + s)^(-1/2) = -1/x^2

Step 5: Multiply both sides by 2 to eliminate the fraction
(x + s)^(-1/2) = -2/x^2

Step 6: Take the derivative of the left-hand side using the chain rule
d/dx [(x + s)^(-1/2)] = d/dx (-2/x^2)

Step 7: Apply the chain rule
(-1/2)(x + s)^(-3/2)(1) = 2(2/x^3)

Step 8: Simplify
-(x + s)^(-3/2) = 4/x^3

Therefore, the derivative of sqrt(x + s) = (1/x) + (1/s) with respect to x is -(x + s)^(-3/2) = 4/x^3.