How to Find a Derivative
To differentiate a polynomial, apply the power rule to each term: the derivative of xⁿ is n xⁿ⁻¹. Constants differentiate to 0.
What is a derivative?
The derivative f′(x) is the limit of [f(x+h) − f(x)] / h as h approaches 0. Geometrically it is the slope of the tangent line.
Step-by-step method
- Write the function as a sum of power terms.
- Multiply each coefficient by the exponent and reduce the exponent by 1.
- The derivative of a constant is 0.
Example
f(x) = x³ + 2x
- 3x² + 2
Answer: 3x² + 2
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Leaving the exponent unchanged
After multiplying by n, the new exponent is n − 1.
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Frequently asked questions
What is d/dx?
It means “differentiate with respect to x.”