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

[madeeeeee]

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!

 

[HallsofIvy]

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
4x^{3/2}- 2\sqrt{x}
or
\frac{4x^3}{2}- 2\sqrt{x}
or
\frac{4x^3}{2- 2\sqrt{x}}?

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!