Find the 3rd Derivative y=1/x

Problem

d3()/(d(x)3)1/x

Solution

1. Rewrite the function using a negative exponent to make differentiation easier.

y=x(−1)

2. Find the first derivative by applying the power rule, which states d(xn)/d(x)=n*x(n−1)

d(y)/d(x)=−1*x(−2)

3. Find the second derivative by differentiating the first derivative with respect to x

d2(y)/(d(x)2)=(−1)*(−2)*x(−3)

d2(y)/(d(x)2)=2*x(−3)

4. Find the third derivative by differentiating the second derivative with respect to x

d3(y)/(d(x)3)=(2)*(−3)*x(−4)

d3(y)/(d(x)3)=−6*x(−4)

5. Simplify the expression by rewriting the negative exponent as a fraction.

d3(y)/(d(x)3)=−6/(x4)

Final Answer

d3()/(d(x)3)1/x=−6/(x4)

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