Calculus practice
Derivatives of Inverse Functions worksheets
Find explicit inverses and differentiate affine, power, rational, logarithmic and exponential inverse pairs with exact domains.
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Find the inverse g = f inverse, then differentiate the explicit inverse directly. State the original, inverse, and derivative domains.
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Customize this worksheetFind the inverse before differentiating
Every worked key swaps the variables, isolates the dependent variable, names the result g, and then differentiates that explicit inverse.
Learning objective
What this activity builds
Swap and isolate to find g = f inverse, then differentiate the explicit inverse directly.
Worked example
Find and differentiate the inverse of f(x) = 2x + 3.
g(x) = (x - 3)/2 and g'(x) = 1/2.
Write x = 2y + 3, isolate y, name that expression g, and then differentiate g directly.
Teaching notes
Make the practice count
- Write y = f(x), swap x and y, then isolate y before differentiating.
- Keep an even-power branch so the original is one-to-one.
- Record derivative-domain exclusions even when the inverse itself exists at an endpoint.
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Choose your options, update the preview, then download the exact same pages.
Choose 15 or 30 problems and use x throughout or cycle through x, t, u, v, w and z. The five function families stay balanced.