Find the Derivative - d/dx (2x)/(x^2)

Problem

d()/d(x)(2*x)/(x2)

Solution

1. Simplify the expression before differentiating by canceling the common factor of x in the numerator and denominator.

(2*x)/(x2)=2/x

2. Rewrite the expression using a negative exponent to prepare for the power rule.

2/x=2*x(−1)

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

(d(2)*x(−1))/d(x)=2*(−1)*x(−1−1)

4. Simplify the resulting expression by performing the multiplication and combining the exponents.

−2*x(−2)

5. Convert the expression back into fraction form for the final result.

−2/(x2)

Final Answer

d()/d(x)(2*x)/(x2)=−2/(x2)

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