Question

Найти D(y): y=7x/√(8-x) - √(3x+2)

Answer 1

Відповідь:

Пояснення:

Answer 2

To find the derivative of y with respect to x, we can use the chain rule and the power rule:

y = 7x/√(8-x) - √(3x+2)

y' = d/dx [7x/√(8-x)] - d/dx [√(3x+2)]

First, let's find the derivative of 7x/√(8-x):

y' = d/dx [7x/√(8-x)] = 7 * d/dx [x/√(8-x)] = 7 * [d/dx (x) * d/dx (8-x)^(-1/2)] = 7 * [1/√(8-x) + x/(8-x)^(3/2)]

Next, let's find the derivative of √(3x+2):

y' = d/dx [√(3x+2)] = (3x+2)^(-1/2) * d/dx (3x+2) = (3x+2)^(-1/2) * 3 = 3/(√(3x+2))

Now we can substitute these expressions into the original equation for y':

y' = 7/[√(8-x)] - 3/[√(3x+2)]

Therefore, the derivative of y with respect to x is D(y) = y' = 7/[√(8-x)] - 3/[√(3x+2)].