Find the Derivative - d/d@VAR f(x)=1/x

Problem

d()/d(x)1/x

Solution

1. Identify the function as a power of x by rewriting the fraction using a negative exponent.

1/x=x(−1)

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

d(x(−1))/d(x)=−1*x(−1−1)

3. Simplify the exponent by performing the subtraction.

−1*x(−1−1)=−x(−2)

4. Rewrite the expression back into fraction form by moving the variable to the denominator.

−x(−2)=−1/(x2)

Final Answer

d()/d(x)1/x=−1/(x2)

Want more problems? Check here!