Find f ' (2) for Simple Derivatives: g(2)=3, g ' (2)=-2, h(2)=-1, h ' (2)=4"

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It's better to just use the differentiation rules.In summary, to find f ' (2), we can use the given values of g(2), g ' (2), h(2), and h ' (2) to determine the derivative of each function. Then, we can use the differentiation rules (such as the sum rule and product rule) to find the derivative of f(x) for each given equation. Finally, we can plug in x=2 into the resulting derivative equations to find f ' (2).
  • #1
physicsguy98
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Find f ' (2) given the following.
g(2) = 3 , g ' (2) = -2
h(2) = -1 , h ' (2) = 4

a. f(x) = 2g(x) + h(x)
b. f(x) = g(x) / h(x)
c. f(x) = 4 - h(x)
d. f(x) = g(x)*h(x)
 
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  • #2


physicsguy98 said:
Find f ' (2) given the following.
g(2) = 3 , g ' (2) = -2
h(2) = -1 , h ' (2) = 4

a. f(x) = 2g(x) + h(x)
b. f(x) = g(x) / h(x)
c. f(x) = 4 - h(x)
d. f(x) = g(x)*h(x)

What have you tried. You have to show some work before we are allowed to give you help.
 
  • #3


I tried using lim(x->c) of f(x) - f(c) / x-c but i end up with lim (x->c) of (2g(x) + h(x) -5)/(x-2) for part (a) and i don't know where to go from there
 
  • #4


Don't you know any differentiation rules other than the limit definition? For example, the constant multiple rule, the sum rule, the product rule, the quotient rule?

The limit definition of the derivative can be used, but it will be a pain for products, and especially quotients.
 

FAQ: Find f ' (2) for Simple Derivatives: g(2)=3, g ' (2)=-2, h(2)=-1, h ' (2)=4"

What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function with respect to its input variables. It is a fundamental tool in calculus and is used to study the behavior of functions.

Why do we need derivatives?

Derivatives are important because they allow us to analyze and understand the behavior of functions. They are used in many fields such as physics, engineering, economics, and statistics to model and solve various problems.

How do I find the derivative of a function?

To find the derivative of a function, you can use the rules of differentiation, such as the power rule, product rule, and chain rule. These rules allow you to find the derivative of a function by manipulating its terms and variables.

What is the difference between a derivative and an integral?

A derivative measures the instantaneous rate of change of a function, while an integral measures the accumulation of that function over a given interval. In other words, a derivative tells us how much a function is changing at a specific point, while an integral tells us the total value of that function over a certain range.

What are some real-world applications of derivatives?

Derivatives have many practical applications in fields such as physics, engineering, economics, and finance. For example, derivatives can be used to model the motion of objects, optimize production processes, and calculate financial risk and pricing. They are also used in machine learning and data analysis to find patterns and make predictions.

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