Derivative Calculator
Differentiate any single-variable function step-by-step. Displays the power rule, product rule, quotient rule, and chain rule with complete algebraic substitutions.
Awaiting Input
Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.
Mastering Differentiation
The derivative measures the instantaneous rate of change of a function with respect to its variable, geometrically representing the slope of the tangent line to the curve at any point.
Frequently Asked Questions
How does this derivative calculator show steps?
The solver breaks down your expression term-by-term, identifying the exact calculus rule used and displaying the intermediate substitution.
What is the power rule for derivatives?
The power rule states that d/dx [x^n] = n * x^(n - 1). For example, the derivative of x³ is 3x².
Can it differentiate trigonometric and logarithmic functions?
Yes, it supports sin(x), cos(x), tan(x), ln(x), e^x, and combinations using the product, quotient, and chain rules.
Can I calculate second and higher-order derivatives?
Yes, you can apply differentiation successively to calculate f''(x) and higher derivatives.
When do you use the product rule versus the chain rule?
Use the product rule when two distinct variable functions are multiplied together, such as x² · sin(x). Use the chain rule when one function is nested inside another (composite function), such as sin(x²) or (3x + 1)⁵, where an 'outside' function wraps an 'inside' function.
Why is the derivative of a constant number always zero?
The derivative represents the instantaneous rate of change (the slope) of a function. A constant value like f(x) = 5 is a flat, horizontal line with zero slope. Because the value never changes as x varies, its rate of change is identically zero: d/dx [c] = 0.