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Year 12 · Calculus
Gradient of a tangent
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
What is the gradient of the tangent to y = 3x³ + 8x + 3 at x = 2?
Differentiate first: f'(x) = 9x^2 + 8. Then substitute x = 2: 9 × (2)^2 + 8 = 44.
Answer: 44
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Watch outReduce the power by exactly 1.
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