Find the Derivative - d/dx f(x) = square root of x+1

Problem

d(√(,x+1))/d(x)

Solution

1. Rewrite the square root expression using a fractional exponent to prepare for differentiation.

√(,x+1)=(x+1)(1/2)

2. Apply the power rule and the chain rule, where the derivative of un is n*u(n−1)⋅d(u)/d(x)

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

3. Differentiate the inner function x+1 which results in 1

d(x+1)/d(x)=1

4. Simplify the expression by multiplying the terms and moving the negative exponent to the denominator.

1/2*(x+1)(−1/2)=1/(2√(,x+1))

Final Answer

d(√(,x+1))/d(x)=1/(2√(,x+1))

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