Compute the derivative of a polynomial using the power rule, with step-by-step work for each term.
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Polynomial
Term 1
Term 2
Term 3
Result
Step-by-step work
2x^3 → 6x^2
d/dx(2x^3) = 3 * 2 * x^(3-1) = 6x^2
3x^2 → 6x
d/dx(3x^2) = 2 * 3 * x^(2-1) = 6x
-5x → -5
d/dx(-5x) = 1 * -5 * x^(1-1) = -5
Also in Calculus
Calculus
A derivative calculator applies the power rule to compute the derivative of a polynomial function term by term. Enter the coefficients and exponents, and see the derivative expression with step-by-step work.
For each term ax^n, the derivative is nax^(n−1). Constants (n=0) have a derivative of zero. The derivative of a sum is the sum of the derivatives.
For example, d/dx(2x³ + 3x² − 5x) = 6x² + 6x − 5.
d/dx(axⁿ) = n·a·x^(n−1)
Power rule for differentiation.
Frequently asked questions
The derivative of any constant is zero because constants do not change with respect to x.
Yes — the power rule applies to all real exponents, including negative and fractional values.
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