Find the derivative of each function using the Rules of Differentiation?

[stinajeana]

1.) g(x)= (1/3x^2)+(x^2sqrt5)+(x/6sqrt7)+(9sqrt8)
2.) G(x)= logbase2(x^2+2x+4)
3.) s(theta)= sec^3(tan theta)

.... I've already solved them. I just want to make sure that I used the right rule and that I solved it right. Any help would be great

 

[Deleted member 4993]

1.) g(x)= (1/3x^2)+(x^2sqrt5)+(x/6sqrt7)+(9sqrt8)
2.) G(x)= logbase2(x^2+2x+4)
3.) s(theta)= sec^3(tan theta)

.... I've already solved them. I just want to make sure that I used the right rule and that I solved it right. Any help would be great

Since you have already solved those - please tell us what did you get! We can tell right or wrong.

 

[stinajeana]

Since you have already solved those - please tell us what did you get! We can tell right or wrong.

I submitted my work already and I didn't feel like re-doing it to make sure I got it right haha so I was hoping somebody would just do it so I could compare it with what I did on my assignment in my head. Does that make sense?

 

[Deleted member 4993]

I submitted my work already and I didn't feel like re-doing it to make sure I got it right haha so I was hoping somebody would just do it so I could compare it with what I did on my assignment in my head. Does that make sense?

No... not to me...

 

[daon2]

I submitted my work already and I didn't feel like re-doing it to make sure I got it right haha so I was hoping somebody would just do it so I could compare it with what I did on my assignment in my head. Does that make sense?

Many universities use things like Web Work or Web Assign, where it only requires the answer be submitted for full credit. Besides that, if you really care about the feedback so much, there should be no problem reproducing your work. You'll get the added benefit of knowing what went wrong should your answers be incorrect!

 

[stinajeana]

Many universities use things like Web Work or Web Assign, where it only requires the answer be submitted for full credit. Besides that, if you really care about the feedback so much, there should be no problem reproducing your work. You'll get the added benefit of knowing what went wrong should your answers be incorrect!

2.) G`(x)= (2x+3)/(x^2+2x+4)ln2
3.) S`(theta)= (sec^3xtanx)(tan theta)+(sec^3)(sec^2x)

.. just trying to remember how I did number one now

 

[mmm4444bot]

2.) G`(x)= (2x+3)/(x^2+2x+4)ln2

I'm thinking that you worked it correctly, but your typing above contains some mistakes.

The 3 is a typo, yes?

Also, without grouping symbols around the entire denominator, the ln(2) ends up in the numerator; that was probably not your intent.

Typing (2x + 2)/[(x^2 + 2x + 4) ln(2)] means \(\displaystyle \displaystyle \frac{2x + 2}{(x^2 + 2x + 4) ln(2)}\)

Otherwise, good job. :cool:

 

[mmm4444bot]

trying to remember how I did number one

g(x)= (1/3x^2)+(x^2sqrt5)+(x/6sqrt7)+(9sqrt8)

As typed, the first exercise is read as follows.

\(\displaystyle \displaystyle g(x) = \frac{1}{3}x^2 + \sqrt{5} x^2 + \frac{\sqrt{7}}{6}x + 9\sqrt{8}\)

That's probably not what you meant to show, as it requires only combining like-terms, simplifying the square root of 8, and then differentiating by applying the power rule term-by-term.

Please check your typing, and use grouping symbols where needed.

Cheers :cool:


Afterthought: No need to simplify the square root before differentiating, as constants go to zero...

 

[mmm4444bot]

3.) S`(theta)= (sec^3xtanx)(tan theta)+(sec^3)(sec^2x)

Hmmm -- I cannot resolve your typing, on this one.

You have mixed θ and x together.

Also, the inputs for the first two secant functions are not clear.

Please proofread your typing. :cool:

 

[stinajeana]

As typed, the first exercise is read as follows.

\(\displaystyle \displaystyle g(x) = \frac{1}{3}x^2 + \sqrt{5} x^2 + \frac{\sqrt{7}}{6}x + 9\sqrt{8}\)

Yeah I meant x to the power of 4sqrt5

....and I don`t quite understand how to write the equations like you do on here

 

[stinajeana]

As typed, the first exercise is read as follows.

\(\displaystyle \displaystyle g(x) = \frac{1}{3}x^2 + \sqrt{5} x^2 + \frac{\sqrt{7}}{6}x + 9\sqrt{8}\)

In words for number 1: (1 divided by 3sqrtx to the power of two) + (x to the power of 4sqrt5) + (x divided by 6sqrt7) + (9sqrt8)

In words for number 3: S(theta)= sec to the power of 3(tan theta)
S`(theta)= (sec `to the power of 3` x)*(tanx) + (sec power of 3)(sec `to the power of 2` x)

 

[mmm4444bot]

I don`t quite understand how to write the equations like you do on here

That system is called LaTex; you may google it for tutorials.

LaTex is a nicety, but it's not necessary. Mathematical expressions may be typed unambiguously, by using grouping symbols.

 

[mmm4444bot]

In words for number 1:

1 divided by 3sqrtx to the power of two

This description is ambiguous.

1/[3*sqrt(x)]^2

1/[3*sqrt(x^2)]

Something else?

If you cannot understand how to type your expressions clearly, please write them on paper, take pictures, and upload the images. (See the FAQ.)

Thank you. :cool:

 

[mmm4444bot]

You may find THIS SITE useful; it explains some basics regarding how to properly type math, using grouping symbols. Cheers :cool: