Derivative Calculator
Calculate derivatives of mathematical functions. Supports polynomial, trigonometric, exponential, and logarithmic functions.

Supports polynomials with x. Use ^ for exponents (e.g., x^2).

f(x)Tangent line
Derivative
f(x) = 3x^2 + 2x - 5
f'(x) = 6x + 2
Step-by-Step Solution
  1. Original: f(x) = 3x^2 + 2x - 5
  2. Apply the power rule: d/dx[x^n] = n·x^(n-1)
  3. d/dx[3x^2] = 2 × 3 × x^(2-1) = 6x
  4. d/dx[2x] = 2
  5. d/dx[-5] = 0 (constant rule)
  6. f'(x) = 6x + 2

Common Derivative Rules

f(x)f'(x)Rule
x^nn·x^(n-1)Power Rule
e^xe^xExponential
ln(x)1/xNatural Log
sin(x)cos(x)Trig
cos(x)-sin(x)Trig
tan(x)sec²(x)Trig

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