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Calcimator

Derivative Calculator

Calculate the derivative of polynomial, trigonometric, exponential, and logarithmic functions at any point.

Inputs

Results

f'(x)

6

Slope at Point6
Tangent y-intercept-4
How to Use This Calculator
  1. Select the Function Type: Polynomial (c·xⁿ), Trigonometric (c·sin(xⁿ)), Exponential (c·eⁿˣ), or Logarithmic (c·n·ln(x)).
  2. Enter the Coefficient (c) and Exponent/Parameter (n) that define the function.
  3. Enter the x Value at which to evaluate the derivative — this is the point of tangency.
  4. The derivative f'(x) represents the instantaneous rate of change (slope of the tangent) at the entered x value.
  5. Tangent y-intercept completes the tangent line equation: y = f'(x₀)·x + b.
  6. The chart plots f(x) and the tangent line near x₀ to visually confirm the slope.

How the result changes with x Value

x Valuef'(x)
-8038,400
-305,400
305,400
8038,400

What each input means

Function Type
Type of function to differentiate
Coefficient (c)
Leading coefficient of the function
Exponent/Parameter (n)
Exponent for polynomial, parameter for trig/exp/log
x Value
Point at which to evaluate the derivative

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Function Type = 1, Coefficient (c) = 2, Exponent/Parameter (n) = 3, x Value = 1 = 4 input(s) provided
  2. Calculate f'
    f'
    6 = 6
  3. Calculate Slope at Point
    Slope at Point
    6 = 6
  4. Calculate Tangent y-intercept
    Tangent y-intercept
    -4 = -4

Engine last updated . Checked against 6 independently-derived tests — how we verify calculators.

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