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Year 12 · Calculus
Derivative at a point
The derivative measures how fast a function changes: the gradient at any point.
How to do it
- Power rule: bring the power down in front, then reduce it by 1.
- The derivative of a constant is 0.
- For the gradient at a point, substitute x into the derivative.
Worked example
If f(x) = 5x² + 3x + 3, find f'(-3).
Differentiate first: f'(x) = 10x + 3. Then substitute x = -3: 10 × (-3)^1 + 3 = -27.
Answer: -27
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Watch outReduce the power by exactly 1.
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