Find Derivatives Step by Step
Calculate derivatives using the power rule, product rule, quotient rule, and chain rule. Evaluate slopes at any point with detailed step-by-step solutions.
How It Works
d/dx(xⁿ) = n·xⁿ⁻¹The power rule states that the derivative of xⁿ is n·xⁿ⁻¹. For example, d/dx(3x²) = 6x. Constants have a derivative of zero. The sum rule allows you to differentiate each term independently.
Quick Tips
Power Rule
d/dx(xⁿ) = n·xⁿ⁻¹ — bring the exponent down, reduce by 1.
Constant Rule
d/dx(c) = 0 — the slope of a flat line is zero.
Evaluate Slope
Enter an x-value to find the exact slope of the tangent line at that point.
Chain Rule
d/dx[f(g(x))] = f'(g(x))·g'(x) — for composite functions.
Step-by-Step Instructions
- 1Enter your function in standard polynomial form (e.g., 3x^2 + 2x - 5).
- 2Optionally enter an x-value to evaluate the derivative at that point.
- 3Click Calculate to see the derivative and step-by-step solution.
Frequently Asked Questions
What is a derivative?▼
A derivative measures the rate of change of a function. It tells you the slope of the tangent line at any point on the curve. If f(x) = x², then f'(x) = 2x — the slope increases as x increases.
What is the power rule?▼
The power rule is d/dx(xⁿ) = n·xⁿ⁻¹. Bring the exponent down as a multiplier and reduce the exponent by 1. For 3x²: derivative = 3·2·x¹ = 6x.
Can I evaluate the derivative at a specific point?▼
Yes! Enter an x-value in the "Evaluate at" field. The calculator will compute f'(x) at that point, giving you the exact slope of the tangent line.