Find the 3rd Derivative f(x)=1/x

Problem

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

Solution

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

ƒ(x)=x(−1)

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

d(ƒ(x))/d(x)=−1*x(−2)

3. Find the second derivative by differentiating the first derivative.

d2(ƒ(x))/(d(x)2)=(−1)*(−2)*x(−3)

d2(ƒ(x))/(d(x)2)=2*x(−3)

4. Find the third derivative by differentiating the second derivative.

d3(ƒ(x))/(d(x)3)=(2)*(−3)*x(−4)

d3(ƒ(x))/(d(x)3)=−6*x(−4)

5. Simplify the expression by moving the variable back to the denominator.

d3(ƒ(x))/(d(x)3)=−6/(x4)

Final Answer

d3()/(d(x)3)1/x=−6/(x4)

Want more problems? Check here!