Reviewed by Yaren Fadiloglulari
Find the derivative of 1/ x?
Answer: The derivative of 1/x is -1/x^2
Finding the derivative of 1/x is a common calculus problem that involves applying the rules of differentiation to rational functions. This concept is important for understanding how functions change and is widely used in mathematical modeling and sciences.
Methods
Math Tutor Explanation Using the Power Rule
Rewrite 1/x as a power of x and apply the power rule for derivatives.
Step 1: Step 1: Rewrite 1/x as x^-1
Step 2: Step 2: Use the power rule: d/dx[x^n] = n*x^(n-1)
Math Tutor Explanation Using the Quotient Rule
Alternatively, use the quotient rule for differentiating a function of the form f(x)/g(x).
Step 1: Step 1: Identify f(x) = 1 and g(x) = x
Step 2: Step 2: Apply the quotient rule: (f/g)' = (f'g - fg')/g^2
Step 1:
Step 2:
Math Tutor suggests: More on Derivatives and Calculus Concepts
Strengthen your calculus skills by exploring related questions on derivatives, antiderivatives, and integrals.
FAQ on Derivatives of Rational Functions
What is the derivative of x^n?
The derivative is n*x^(n-1)
Why is the derivative of 1/x negative?
Because increasing x makes 1/x smaller, so the slope is negative
Can you use the product rule on 1/x?
Not directly, but you can rewrite 1/x as x^-1 and differentiate
What is the integral of 1/x?
The integral is ln|x| + C
Does this derivative apply for all x?
No, it applies for all x except x = 0, where 1/x is undefined
Winter Math & Reading Camp for Grades 1-9
Join Brighterly's Online Winter Camp to excel in math and reading.
Choose kid's grade
Winter Math & Reading Camp for Grades 1-9
Join our Winter Camp, boost your child's math and reading skills.