Derivative Calculator
Find the derivative of a function.
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Find the Derivative of a Function
Our Derivative Calculator helps you compute the derivative of a mathematical function with respect to a variable, showing the step-by-step differentiation process.
What is a Derivative Calculator?
A Derivative Calculator is a computational tool that performs symbolic differentiation, a fundamental operation in calculus. It takes a mathematical function and a variable, and applies the rules of differentiation to find the function that describes the instantaneous rate of change. This is invaluable for students learning calculus and for engineers and scientists who need to solve complex problems involving rates of change.
How It Works: Applying Differentiation Rules
The calculator uses a powerful computer algebra system to parse your input function and apply the appropriate differentiation rules, such as:
Power Rule: d/dx(xⁿ) = nxⁿ⁻¹
Product Rule: d/dx(uv) = u(dv/dx) + v(du/dx)
Chain Rule: d/dx(f(g(x))) = f'(g(x))g'(x)
Frequently Asked Questions
How do you calculate a derivative?
Derivatives are calculated using a set of rules, such as the power rule, product rule, quotient rule, and chain rule. The power rule, for example, states that the derivative of xⁿ is nxⁿ⁻¹. Our calculator applies these rules automatically to find the derivative of a given function.
What is a derivative?
In calculus, a derivative represents the instantaneous rate of change of a function with respect to one of its variables. Geometrically, it represents the slope of the tangent line to the function's graph at a specific point.
What is the derivative of x^2?
Using the power rule, the derivative of x² is 2x.
What does a second derivative tell you?
The second derivative of a function tells you about its concavity. If the second derivative is positive, the function is concave up (like a smile). If it's negative, the function is concave down (like a frown). Points where the second derivative is zero can be inflection points.
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