- #1
s883
- 5
- 0
Homework Statement
Could anyone explain me how to solve this?
Homework Equations
f(x) =
1/x2 + 4x + 9 + x4 , f’”’(-2) =
Understanding Differential Calculus: Solving Homework Equations
- Thread starter s883
- Start date
In summary, differential calculus is a branch of mathematics that focuses on the study of change in a function. It involves finding the instantaneous rate of change of a function at a given point and determining the slope of a tangent line at any point on a curve. It differs from integral calculus, which deals with the accumulation of quantities over a given interval. Some real-world applications of differential calculus include physics, engineering, economics, and statistics. The fundamental concepts in differential calculus are limits, derivatives, and differentiability. To learn differential calculus, a strong foundation in algebra and trigonometry is necessary, and studying through textbooks, online courses, or with the help of a tutor is recommended. Regular practice and thorough understanding of the concepts are crucial for mastering the
Could anyone explain me how to solve this?
f(x) =
1/x2 + 4x + 9 + x4 , f’”’(-2) =
- #2
Saladsamurai
- 3,020
- 7
Hello s883! 
It means to take the 4th derivative of the given function f(x) and then evaluate the resulting expression at x = -2. And I would probably put calculus questions in the calculus forum for next time
It means to take the 4th derivative of the given function f(x) and then evaluate the resulting expression at x = -2. And I would probably put calculus questions in the calculus forum for next time - #3
HallsofIvy
Science Advisor
Homework Helper
- 42,989
- 975
I assume you mean [itex]f(x) = 1/x^2 + 4x + 9 + x^4= x^{-2}+ 4x+ 9+ x^4[/itex].
Can you find f'(x) using the "power rule" ([itex](x^n)'= n x^{n-1}[/itex])?
What about f'' and f'''?
Now do f''''.
Can you find f'(x) using the "power rule" ([itex](x^n)'= n x^{n-1}[/itex])?
What about f'' and f'''?
Now do f''''.
What is differential calculus?
Differential calculus is a branch of mathematics that deals with the study of change in a function. It involves finding the instantaneous rate of change of a function at a given point, as well as determining the slope of a tangent line at any point on a curve.
What is the difference between differential calculus and integral calculus?
Differential calculus focuses on the study of rates of change, whereas integral calculus deals with the accumulation of quantities over a given interval. In other words, differential calculus is concerned with the slope of a curve, while integral calculus is concerned with the area under a curve.
What are some real-world applications of differential calculus?
Differential calculus has many practical applications, such as in physics, engineering, economics, and statistics. It is used to analyze motion, optimize functions, and solve problems involving rates of change, such as finding maximum and minimum values.
What are the basic concepts in differential calculus?
The fundamental concepts in differential calculus include limits, derivatives, and differentiability. Limits are used to describe the behavior of a function as the input approaches a specific value, while derivatives measure the instantaneous rate of change of a function at a given point. Differentiability refers to the smoothness of a function, which is necessary for it to have a well-defined derivative.
How can I learn differential calculus?
To learn differential calculus, it is essential to have a strong foundation in algebra and trigonometry. You can study it through textbooks, online courses, or with the help of a tutor. It is also crucial to practice solving problems and understanding the concepts thoroughly to master the subject.
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