High School Derivative Calculator
Enter a function to compute its symbolic derivative f'(x) using the Chain, Product, and Quotient rules.
Try: x^2 * sin(x) (Product), (x+1)/(x-1) (Quotient), sin(x^2) (Chain)
Symbolic Derivative f'(x)
Slope at Point x
Analysis
Ready to differentiate.
Calculus Graph
Understanding the Derivative Calculator
Calculus is the mathematical study of continuous change. The derivative of a function measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Graphically, the derivative at a point is the slope of the tangent line to the graph of the function at that point.
Key Differentiation Rules
- Power Rule: If f(x) = x^n, then f'(x) = nx^(n-1).
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Product Rule: Used when differentiating a product of two functions.
(fg)’ = f’g + fg’ -
Quotient Rule: Used for division of functions.
(f/g)’ = (f’g – fg’) / g^2 -
Chain Rule: Used for composite functions.
f(g(x))’ = f'(g(x)) * g'(x)
Why use a Derivative Calculator?
While learning the manual rules is essential for exams, applying the Chain Rule nested inside a Quotient Rule can become messy and error-prone. This tool provides an instant check for your homework results. It not only gives the symbolic answer but also visualizes the relationship between the function and its slope, which is key to intuition.
FAQ
Yes, this is a free educational resource for students.
It represents an infinitesimally small change in x. The derivative dy/dx is the ratio of these tiny changes.
Yes! You can use sin, cos, tan, sec, csc, cot, log, exp, and sqrt.
The calculator attempts to simplify the expression, but some derivatives naturally expand into long algebraic strings.