Mathematics
Derivatives
A derivative measures instantaneous rate of change — the slope of a curve at a point. Once you know a few rules (power, product, chain, quotient), you can differentiate almost any function.
How to Approach Derivatives
Identify the function type
Is it a polynomial, product of two functions, composition, or a quotient? The method depends on the structure.
Apply the rule
Power rule: d/dx[xⁿ] = n·x^(n-1). Product: (fg)' = f'g + fg'. Chain: (f(g))' = f'(g)·g'. Quotient: (f/g)' = (f'g - fg')/g².
Simplify
Combine like terms, factor where possible. ScanSolve shows the algebra so you can see exactly where each step came from.
Frequently Asked Questions
What does dy/dx mean?+
It's the derivative of y with respect to x — the instantaneous rate at which y changes per unit change in x. Geometrically: the slope of the tangent line to the graph of y(x).
When do I use the chain rule?+
When you're differentiating a composition: f(g(x)). The derivative is f'(g(x)) · g'(x). Examples: sin(x²), e^(3x+1), √(x² + 1).
Are partial derivatives different?+
Partial derivatives apply to multi-variable functions. ∂f/∂x treats every other variable as a constant. ScanSolve handles partials with full step-by-step too.
Related Topics
More step-by-step guides in Mathematics and adjacent subjects.
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