Find dy/dx y = square root of x

Problem

d()/d(x)√(,x)

Solution

1. Rewrite the square root as a power using the rule √(,x)=x^(1/2)

y=x^(1/2)

2. Apply the power rule for differentiation, which states that d(x^n)/d(x)=n*x^(n−1)

d(y)/d(x)=1/2*x^(1/2−1)

3. Simplify the exponent by performing the subtraction.

d(y)/d(x)=1/2*x^(−1/2)

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

d(y)/d(x)=1/(2√(,x))

Final Answer

d(√(,x))/d(x)=1/(2√(,x))

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