Derivative Calculator
Power Rule (d/dx xⁿ)
Find the derivative of xⁿ using the power rule
Polynomial Derivative (ax³ + bx² + cx + d)
Find the derivative of a cubic polynomial
Trigonometric Derivative
Find derivatives of common trig functions
Exponential / Logarithmic Derivative
Find derivatives of eˣ, aˣ, ln(x), log(x)
Formula
Power: d/dx [xⁿ] = nxⁿ⁻¹ | Product: (fg)' = f'g + fg' | Chain: d/dx [f(g(x))] = f'(g(x))·g'(x)
Frequently Asked Questions
What is a derivative?
A derivative measures the rate of change of a function. f'(x) = lim(h→0) [f(x+h) - f(x)] / h. It gives the slope of the tangent line at any point on the curve.
What is the power rule?
The power rule states: d/dx [xⁿ] = n·x^(n-1). Multiply by the exponent, then reduce the exponent by 1. For example, d/dx [x³] = 3x².
What is the chain rule?
The chain rule is used for composite functions: d/dx [f(g(x))] = f'(g(x)) · g'(x). For example, d/dx [sin(3x)] = cos(3x) · 3 = 3cos(3x).
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