Derivatives measure how functions change and are fundamental to calculus, physics, engineering, and economics. Whether you're computing the slope of a tangent line or finding rates of change, Solver AI's derivative calculator provides instant, detailed solutions for any differentiation problem.
Our calculator handles all differentiation techniques: basic power rule, product rule, quotient rule, chain rule, implicit differentiation, logarithmic differentiation, partial derivatives, and higher-order derivatives. It works with polynomial, trigonometric, exponential, logarithmic, and composite functions.
Learning to differentiate requires understanding which rule to apply and when. Solver AI doesn't just compute the derivative—it identifies the function type, selects the appropriate differentiation technique, and walks you through each application of the rule. This builds the problem-solving skills you need for exams and advanced coursework.
From finding critical points and inflection points to analyzing function behavior with first and second derivative tests, Solver AI supports the full range of derivative applications. Photograph your problem or enter a function to get a complete, step-by-step differentiation.
Derivative mistakes usually involve missing a rule. Many students forget to apply the chain rule when there is a function inside another function — the derivative of sin(2x) is 2cos(2x), not cos(2x). Others use the power rule on functions where it does not apply, or forget that the derivative of a constant is zero. The product rule and quotient rule must be applied carefully because skipping a term changes the answer entirely. Rewriting expressions using algebra often makes derivatives much easier and less error-prone.
Identify the structure of the function before differentiating. If you see a product of two functions, use the product rule. If you see one function inside another, use the chain rule. If you see a quotient, decide whether to use the quotient rule or rewrite as a product with a negative exponent. Always simplify the original function first if possible — sometimes a quick algebraic rewrite turns a hard derivative into a one-line answer that takes seconds rather than minutes.
Derivatives describe rates of change, which appear everywhere. In physics, the derivative of position is velocity and the derivative of velocity is acceleration. In economics, marginal cost and marginal revenue are derivatives. In biology, derivatives describe how populations grow or decline. Even artificial intelligence relies on derivatives — neural networks learn by computing gradients (multivariable derivatives) of their loss function. Mastering derivatives gives you the language to describe how anything changes over time, in any quantitative field.
Solution: f'(x) = 12x³ - 4x + 1 (power rule)
Solution: 2x·cos(x²) using chain rule
Solution: 2x·ln(x) + x using product rule
Solution: y' = 3x² - 6, y'' = 6x
Solver AI supports the power rule, product rule, quotient rule, chain rule, implicit differentiation, logarithmic differentiation, and can compute partial and higher-order derivatives.
Yes! Solver AI can compute second, third, and higher-order derivatives with full step-by-step solutions for each differentiation.
Absolutely. Solver AI applies implicit differentiation to equations where y is defined implicitly as a function of x, showing every step of the process.
Yes! Take a photo of any derivative problem, including those with complex notation like fractions and exponents, and Solver AI will solve it step by step.