What is the derivative of the function?

In summary, the conversation revolves around finding the derivative of the function f(t) = 100t/2t+15, with one person requesting help and the other asking for clarification and showing potential solutions. The main focus is on whether the expression should be written as f(t) = 100t/(2t+15) or f(t) = (100t/2t) + 15. The conversation also touches on using the quotient rule to find the derivative.
  • #1
elton_fan
16
0
hi all
i need a derivative of this function f(t)=100t/2t+15


thanks a lot
 
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  • #2
You need to show us your attempt. Are you familiar with the quotient rule and so on?
 
  • #3
FYI, you wrote

[tex]
f(t)=\frac{100t}{2t}+15
[/tex]

Is that what you meant? If you meant to write

[tex]
f(t)=\frac{100t}{2t+15}
[/tex]

then you need to use parentheses.
 
  • #4
Hurkyl said:
FYI, you wrote

[tex]
f(t)=\frac{100t}{2t}+15
[/tex]

Is that what you meant? If you meant to write

[tex]
f(t)=\frac{100t}{2t+15}
[/tex]

then you need to use parentheses.

I'm almost certain he means the later, or the answer is pretty basic in fact it barely requires calculus.:smile:

[tex]
f(t)=\frac{100t}{2t+15}
[/tex]

Have you tried the quotient rule? Please show working?
 

FAQ: What is the derivative of the function?

What is differentiation of a function?

Differentiation of a function is a mathematical process of finding the rate of change of the function with respect to its independent variable. It involves finding the slope of the tangent line at a given point on the function's graph.

Why is differentiation important?

Differentiation is important because it allows us to understand the behavior of a function and its rate of change. It is used in various fields such as physics, engineering, economics, and statistics to analyze and solve real-world problems.

What is the difference between differentiation and integration?

Differentiation and integration are inverse operations of each other. Differentiation involves finding the rate of change of a function, while integration involves finding the area under the curve of a function.

How do you differentiate a function?

To differentiate a function, you can use the power rule, product rule, quotient rule, or chain rule, depending on the form of the function. These rules involve taking the derivative of the function, which is essentially finding the slope of the tangent line at a given point.

What are the applications of differentiation in real life?

Differentiation has numerous applications in real life, such as in physics to find the velocity and acceleration of an object, in economics to determine the marginal cost and revenue, and in biology to analyze growth and decay of populations. It is also used in optimization problems to find the maximum or minimum value of a function.

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