Find dy/dx y=1/x

Problem

d()/d(x)1/x

Solution

1. Rewrite the expression using a negative exponent to make it easier to differentiate.

y=x(−1)

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

d(y)/d(x)=−1⋅x(−1−1)

3. Simplify the exponent by performing the subtraction.

d(y)/d(x)=−x(−2)

4. Rewrite the result using a positive exponent by moving the variable back to the denominator.

d(y)/d(x)=−1/(x2)

Final Answer

d()/d(x)1/x=−1/(x2)

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