find the derivative of each of the following

Question

1)f(x)=(3x²+5)(2x-1)

 

2) f(x)=6x-11/8x+1

 

3) f(x)=(5x-2)(2x+3)/x-4

 

4)f(x)=(8x+3)²

 

5) f(x)=√¯8-5x

 

6) f(x)-6x(7x-1)²

 

7) f(x)=-6e^x+1

 

8) f(x) =1n(5x²-3x)

 

9)f(x)=5x²/e^x

Answer 1

Hi Stephanie,

 

I could do these problems for you and you would do really well on this homework, but you would not have learned anything from it.  Why don't you try them and ask questions about why you are not getting the right answer.  I would be happy to help.  i will solve number 8 for you as it is one of the more difficult ones.

 

8) f(x) = ln (5x^2-3x)

 

To take the derivative you first need to take the derivative of the ln function.  

 

The derivative of ln(x) is 1/x.  

 

Thus step one of the derivative is 1/(5x^2-3x),

 

 

but we also need to take the derivative of what was inside the ln function or (5x^2-3x) which is (10x-3)

 

then we have to multiply it by the first part which was 1/(5x^2-3x).

 

So finally f'(x) = (10x-3)/(5x^2-3x)

 

I hope this helps.  Best of luck with calculus this year.

 

Sincerely,

Ralph K.