Airplane takeoff Suppose that the distance an aircraft travels along a runway before takeoff is given by D = (10/9)t², where D is measured in meters from the starting point and t is measured in seconds from the time the brakes are released. The aircraft will become airborne when its speed reaches 200 km/h. How long will it take to become airborne, and what distance will it travel in that time?
Table of contents
- 0. Functions7h 52m
- Introduction to Functions16m
- Piecewise Functions10m
- Properties of Functions9m
- Common Functions1h 8m
- Transformations5m
- Combining Functions27m
- Exponent rules32m
- Exponential Functions28m
- Logarithmic Functions24m
- Properties of Logarithms34m
- Exponential & Logarithmic Equations35m
- Introduction to Trigonometric Functions38m
- Graphs of Trigonometric Functions44m
- Trigonometric Identities47m
- Inverse Trigonometric Functions48m
- 1. Limits and Continuity2h 2m
- 2. Intro to Derivatives1h 33m
- 3. Techniques of Differentiation3h 18m
- 4. Applications of Derivatives2h 38m
- 5. Graphical Applications of Derivatives6h 2m
- 6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
- 7. Antiderivatives & Indefinite Integrals1h 26m
- 8. Definite Integrals4h 44m
- 9. Graphical Applications of Integrals2h 27m
- 10. Physics Applications of Integrals 3h 16m
- 11. Integrals of Inverse, Exponential, & Logarithmic Functions2h 34m
- 12. Techniques of Integration7h 39m
- 13. Intro to Differential Equations2h 55m
- 14. Sequences & Series5h 36m
- 15. Power Series2h 19m
- 16. Parametric Equations & Polar Coordinates7h 58m
3. Techniques of Differentiation
Basic Rules of Differentiation
Struggling with Calculus?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Find the indicated derivative.
d/dx(π)
A
0
B
π
C
1
D
x

1
Recognize that \( \pi \) is a constant. In calculus, the derivative of a constant with respect to any variable is always zero.
Apply the rule for the derivative of a constant: \( \frac{d}{dx}(c) = 0 \), where \( c \) is a constant.
Since \( \pi \) is a constant, use the rule: \( \frac{d}{dx}(\pi) = 0 \).
Understand that this result is consistent with the fact that constants do not change, and thus their rate of change (derivative) is zero.
Conclude that the derivative of \( \pi \) with respect to \( x \) is \( 0 \).
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Basic Rules of Differentiation practice set
