Find Derivatives of Functions: Simplified Answers for f(x), g(x), and y

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In summary, the derivative of f(x) = Square root of 3x + 2 is 1/(2(square root of 3x+2)). The derivatives of the given functions are not correct and further clarification is needed in order to provide the correct answers.
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madeeeeee
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1. the definition of a derivative as limit, find f'(x) given f(x) = Square root of 3x + 2

Answer:

lim Square root of 3(x+h) - the sqaure root of 3x+2 / h
h-> 0

lim Square root of 3x+3h +2 - the sqaure root of 3x+2 /h
h-> 0

final answer: 1/ (2)(sqaure root of 3x+ 2

8. Find the derivatives of the following functions. Simplify!

a) f(x)= 4x^3/2 - (2)(squr root x)

answer: (-6) / (squr root of x)

b) g(x)= 3/x^2 + 6x^-3/2 - x

answer: = -6x^-3 - 9x^-5/2

e) y= x^3 / x^2 + 9

= 3x^2 / -2x

Are these right? Thx!
 
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  • #2
madeeeeee said:
1. the definition of a derivative as limit, find f'(x) given f(x) = Square root of 3x + 2

Answer:

lim Square root of 3(x+h) - the sqaure root of 3x+2 / h
h-> 0

lim Square root of 3x+3h +2 - the sqaure root of 3x+2 /h
h-> 0

final answer: 1/ (2)(sqaure root of 3x+ 2
No, that is not correct. How did you get it?

8. Find the derivatives of the following functions. Simplify!

a) f(x)= 4x^3/2 - (2)(squr root x)
Is this intended to be
[tex]4x^{3/2}- 2\sqrt{x}[/tex]
or
[tex]\frac{4x^3}{2}- 2\sqrt{x}[/tex]
or
[tex]\frac{4x^3}{2- 2\sqrt{x}}[/tex]?

answer: (-6) / (squr root of x)
No, none of those possible functions has this derivative.

b) g(x)= 3/x^2 + 6x^-3/2 - x

answer: = -6x^-3 - 9x^-5/2
No, again, that is not correct.

e) y= x^3 / x^2 + 9
What you have written is y= x+ 9 which is surely not what you mean!

= 3x^2 / -2x
Assuming you meant x^3/(x^2+ 9), no it is not.

Are these right? Thx!
You have every single one of these wrong! If you want help, you will have to show how you are attempting these!
 

FAQ: Find Derivatives of Functions: Simplified Answers for f(x), g(x), and y

What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is calculated as the slope of the tangent line to the curve of the function at that point.

What is the purpose of taking a derivative?

The main purpose of taking a derivative is to find the rate of change of a function at a specific point. It is also used to find maximum and minimum values of a function, as well as the concavity of a curve.

How do I find the derivative of a function?

To find the derivative of a function, you need to use the rules of differentiation. These include the power rule, product rule, quotient rule, and chain rule. You will also need to know the basic derivatives of common functions.

What is the difference between the derivative and the integral?

The derivative and the integral are two opposite operations in calculus. While the derivative represents the rate of change of a function, the integral represents the accumulation of a function over a given interval. In simpler terms, the derivative measures how fast a function is changing, while the integral measures the total amount of change.

Why is it important to check my derivative answers?

It is important to check your derivative answers because even a small mistake in the calculation can result in a significantly different answer. Checking your work can help you catch any errors and ensure the accuracy of your solution.

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