Question

find the differentiation of (root x -3x)(x+1/x)​

Answer 1

Answer

y' = 1/(2(x - 1)^(1/2)) + 1/(2(x + 1)^(1/2))

Explanation:

We will have to apply the chain rule twice to this problem.

Step 1: Determine the derivative of y = sqrt(x - 1)

Let y = u^(1/2) and u = x - 1

Then dy/dx = 1/2u^(-1/2) xx 1 = 1/(2(x - 1)^(1/2))

Step 2: Determine the derivative of y = sqrt(x + 1)

Let y = u^(1/2) and u = x+ 1#

Then dy/dx = 1/2u^(-1/2) xx 1 = 1/(2(x + 1)^(1/2))

Step 3: Combine the two derivatives using the sum rule

y' = 1/(2(x - 1)^(1/2)) + 1/(2(x + 1)^(1/2))

Answer 2

$\huge \underline \pink {answer}$

y' = 1/(2(x - 1)^(1/2)) + 1/(2(x + 1)^(1/2))

We will have to apply the chain rule twice to this problem.

Step 1: Determine the derivative of y = sqrt(x - 1)

Let y = u^(1/2) and u = x - 1

Then dy/dx = 1/2u^(-1/2) xx 1 = 1/(2(x - 1)^(1/2))

Step 2: Determine the derivative of y = sqrt(x + 1)

Let y = u^(1/2) and u = x+ 1#

Then dy/dx = 1/2u^(-1/2) xx 1 = 1/(2(x + 1)^(1/2))

Step 3: Combine the two derivatives using the sum rule

y' = 1/(2(x - 1)^(1/2)) + 1/(2(x + 1)^(1/2))