Find dy/dx y square root of x+1=4

Problem

y√(,x+1)=4

Solution

1. Rewrite the equation to isolate y by dividing both sides by √(,x+1)

y=4/√(,x+1)

2. Express the square root as a power with a negative exponent to prepare for the power rule.

y=4*(x+1)(−1/2)

3. Apply the chain rule and the power rule to differentiate the expression with respect to x

d(y)/d(x)=4⋅(−1/2)*(x+1)(−3/2)⋅d(x+1)/d(x)

4. Simplify the coefficients and the derivative of the inner function.

d(y)/d(x)=−2*(x+1)(−3/2)⋅1

5. Rewrite the expression using radical notation and positive exponents.

d(y)/d(x)=−2/((x+1)(3/2))

Final Answer

d(y)/d(x)=−2/√(,(x+1)3)

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