Derivative Calculator
Find the derivative of functions and see the step-by-step solution using the rules of differentiation.
Understanding the Rules of Differentiation
The Power Rule
The Power Rule is the most fundamental rule of differentiation. It's used for terms in the form `ax^n`.
Rule: `d/dx (x^n) = n * x^(n-1)`
Example: The derivative of `x^3` is `3x^2`.
The Sum/Difference Rule
This rule states that you can differentiate a function term by term. The derivative of a sum is the sum of the derivatives.
Rule: `d/dx (f(x) + g(x)) = f'(x) + g'(x)`
The Constant Rule
The derivative of any constant number is always zero. This is because a constant doesn't change, so its rate of change is 0.
Rule: `d/dx (c) = 0`
Example: The derivative of `7` is `0`.
Frequently Asked Questions
What is a derivative?
In simple terms, the derivative of a function measures the sensitivity to change of the function's value with respect to a change in its argument. For a function graphed on a 2D plane, the derivative at a point is the slope of the tangent line to the curve at that point.
What does f'(x) mean?
f'(x), read as "f prime of x", is one of the most common notations for the derivative of a function f(x). Another common notation is `d/dx`, which means "the derivative with respect to x".
How do you find the derivative of x^2?
Using the Power Rule, where n=2. The rule is `d/dx (x^n) = n * x^(n-1)`. So, for x², you bring the power (2) down as a multiplier and subtract one from the power: `2 * x^(2-1)`, which simplifies to `2x`.
What functions does this calculator support?
Currently, this calculator is designed to differentiate polynomial functions (e.g., `4x^3 - x^2 + 5`). It supports the power rule, constant multiple rule, sum rule, and constant rule. Support for more complex functions like trigonometric, exponential, and logarithmic functions will be added in the future.