Find the Derivative - d/dx y=5/x

Problem

d()/d(x)5/x

Solution

1. Rewrite the expression using a negative exponent to make it easier to apply the power rule.

5/x=5*x(−1)

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

(d(5)*x(−1))/d(x)=5*(−1)*x(−1−1)

3. Simplify the resulting expression by performing the multiplication and subtraction in the exponent.

−5*x(−2)

4. Convert the expression back into fraction form by moving the variable with the negative exponent to the denominator.

−5/(x2)

Final Answer

d()/d(x)5/x=−5/(x2)

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