Students determine derivatives from first principles using the difference quotient and apply linearity, power, trigonometric, exponential, and logarithmic differentiation rules to familiar functions, including appropriate domains and radians for trigonometric functions. They differentiate products, quotients, and composite functions using the product, quotient, and chain rules, including standard algebraic, trigonometric, exponential, and logarithmic combinations. They compute second, third, and higher-order derivatives when patterns are clear, interpreting the second derivative through concavity and acceleration while excluding multivariable, inverse, hyperbolic, variable-base, and advanced generalized differentiation.
On this page:
- Master skills like “Differentiate power functions”, “Determine higher-order derivatives”, and “Differentiate sums and differences” with unlimited, free practice problems
- Download (or modify) free worksheets on Derivatives you can use at home or in class with practice problems across all skills in this group including “Differentiate exponential functions”, “Differentiate logarithmic functions”, “Differentiate trigonometric functions”.
- Start working on adaptive units like “Basic Derivatives - Practice” or “Derivative Rules - Practice” that include these skills and will introduce and scaffold the skills carefully for maximum learning.
Derivatives: Individual Skills
Master 9 individual skills with free practice problems. Mouseover to see the skill's practice problems. Create a free account to track your progress.
Your results
- Determine higher-order derivatives
- Differentiate composite functions using the chain rule
- Differentiate exponential functions
- Differentiate logarithmic functions
- Differentiate power functions
- Differentiate products using the product rule
- Differentiate quotients using the quotient rule
- Differentiate sums and differences
- Differentiate trigonometric functions
Practice 'Determine higher-order derivatives'
Select any skill in this group by hovering over the list above. Unlimited free practice problems, automatically graded.
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Download/Modify Free Grade 12 'Derivatives' Worksheet
Print this free 'Derivatives' worksheet to practice these skills away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Determine higher-order derivatives
- Differentiate composite functions using the chain rule
- Differentiate exponential functions
- Differentiate logarithmic functions
- Differentiate power functions
- Differentiate products using the product rule
- Differentiate quotients using the quotient rule
- Differentiate sums and differences
Units Teaching These Skills
These adaptive units introduce, teach, or reinforce skills in this group (Derivatives) through scaffolded problems that grow in difficulty as concepts are understood.
Explore More Grade 12 Math
- Applications of Derivatives
- Counting and Probability
- Exponential and Logarithmic Functions
- Financial Mathematics
- Function Characteristics
- Function Transformations and Compositions
- Lines and Planes
- Matrices
- Polynomial and Rational Functions
- Probability Distributions
- Rates of Change and Limits
- Statistical Analysis