- #1
janemba
- 39
- 0
how do you find the derivative of this problem and what rule do you use
lim sin(pi+h)-Sin pi
h-> 0 h
lim sin(pi+h)-Sin pi
h-> 0 h
How do you find a dervative of this
- Thread starter janemba
- Start date
In summary, A derivative is a mathematical tool used to measure how a function changes as its input changes. It represents the slope of a curve at a specific point and can be used to find the rate of change of a function. The process of finding a derivative involves using mathematical rules and formulas to calculate the slope of a function at a given point. This can be done by finding the limit of the slope of a secant line as it approaches a point on the function, or by using specific rules such as the power rule, product rule, or chain rule. A derivative measures the rate of change of a function, while an antiderivative is the inverse operation of a derivative and represents the original function. In other words, a derivative tells
- #2
tiny-tim
Science Advisor
Homework Helper
- 25,839
- 258
… sinπ = 0 …
Hi janemba!
Do you mean [tex]\frac{sin(\pi + h) -sin\pi}{h}[/tex] ?
If so, remember that sinπ = 0, so it's just [tex]\frac{sin(\pi + h)}{h}\,.[/tex]
Which is … ?
Hi janemba!
Do you mean [tex]\frac{sin(\pi + h) -sin\pi}{h}[/tex] ?
If so, remember that sinπ = 0, so it's just [tex]\frac{sin(\pi + h)}{h}\,.[/tex]
Which is … ?
- #3
janemba
- 39
- 0
yes but how did you got the answer
- #4
rocomath
- 1,755
- 1
How do you expand:
[tex]sin(x+y)=?[/tex]
Trig identity ...
[tex]sin(x+y)=?[/tex]
Trig identity ...
- #5
Gib Z
Homework Helper
- 3,351
- 7
It's even simpler than that, take a look at a unit circle and think about what happens with every rotation of pi radians.
1. What is a derivative?
A derivative is a mathematical tool used to measure how a function changes as its input changes. It represents the slope of a curve at a specific point and can be used to find the rate of change of a function.
2. How do you find a derivative?
The process of finding a derivative involves using mathematical rules and formulas to calculate the slope of a function at a given point. This can be done by finding the limit of the slope of a secant line as it approaches a point on the function, or by using specific rules such as the power rule, product rule, or chain rule.
3. What is the difference between a derivative and an antiderivative?
A derivative measures the rate of change of a function, while an antiderivative is the inverse operation of a derivative and represents the original function. In other words, a derivative tells us how a function changes, while an antiderivative tells us what the function is.
4. Why do we need derivatives?
Derivatives are essential in many areas of science, including physics, engineering, economics, and more. They help us understand the behavior and properties of functions, make predictions and projections, and optimize processes and systems.
5. What are some real-world applications of derivatives?
Some common real-world applications of derivatives include finding maximum or minimum values of a function, calculating velocity and acceleration in physics, determining marginal cost and revenue in economics, and optimizing production processes in engineering.
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