Question

Let √u+√2v+1)=5.
Find du/dv .

Answer 1

To find du/dv, differentiate the equation with respect to v using the chain rule.

Step-by-step explanation:

To find du/dv, we need to differentiate the given equation with respect to v.

Let's take the equation: √u + √(2v+1) = 5.

First, let's isolate √u by subtracting √(2v+1) from both sides:

√u = 5 - √(2v+1).

Square both sides to get rid of the square root:

u = (5 - √(2v+1))^2.

Now we can differentiate both sides with respect to v using the chain rule:

du/dv = 2(5 - √(2v+1)) * (d/dv (5 - √(2v+1))).

Simplifying the equation gives:

du/dv = 2(5 - √(2v+1)) * (-√2).

So, du/dv = -2√2(5 - √(2v+1)).