Find the Derivative - d/dx y = square root of x+12

Problem

d()/d(x)√(,x+12)

Solution

1. Rewrite the square root expression using a fractional exponent to make it easier to differentiate.

√(,x+12)=(x+12)(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+12)/d(x)=1/2*(x+12)(−1/2)⋅d(x+12)/d(x)

3. Differentiate the inner function x+12 with respect to x

d(x+12)/d(x)=1

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

1/2*(x+12)(−1/2)⋅1=1/(2√(,x+12))

Final Answer

d(√(,x+12))/d(x)=1/(2√(,x+12))

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