Calculus practice
Evaluate Derivatives at Points worksheets
Differentiate polynomial, rational, exponential and trigonometric functions, then evaluate exactly at a given point.
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Differentiate each function, then evaluate at the given exact point.
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Customize this worksheetDifferentiate, evaluate, then build the line
Every problem gives an exact input. Keep fractions, radicals, pi, powers of e and logarithms exact while finding the point and slope.
Learning objective
What this activity builds
Evaluate exact derivative values at specified inputs.
Worked example
For f(x) = x² + 1, find f'(2).
f'(x) = 2x, so f'(2) = 4.
Differentiate first, evaluate both the function and derivative at the specified input, then use the exact point and slope.
Teaching notes
Make the practice count
- Keep fractions, radicals, pi, e and logarithms exact.
- Use the original function to find the point on the curve.
- For a normal line, check whether the tangent is horizontal before taking a negative reciprocal.
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Choose your options, update the preview, then download the exact same pages.
Choose 6, 8, or 10 problems and one or more polynomial, rational, exponential or trigonometric families. Exact answers retain fractions, radicals, pi, e and logarithms.