A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Can someone please help me find the derivative of this problem? I will fan and medal.
anonymous
 one year ago
Can someone please help me find the derivative of this problem? I will fan and medal.

This Question is Closed

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4Whats the function?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 2 }{ 3 }\sin^\frac{ 3 }{ 2 }x\frac{ 2 }{ 7 }\sin^\frac{ 7 }{ 2 }x\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4\[\frac{2}{3}\left(\sin^{2/3}x\right)' \iff \frac{2}{3}\left((\sin(x))^{2/3}\right)'\]

wmj259
 one year ago
Best ResponseYou've already chosen the best response.0If you look carefully you see that the two functions are connected with the subtract sign. So you can break that function into 2 separate derivatives.

wmj259
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ d }{ dx } (\frac{ 2 }{ 3 }\sin ^{2/3}(x))  \frac{ d }{ dx }((\frac{ 2 }{ 7 }\sin ^{7/2}x))\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4Use the power rule, then the chain rule.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait. How did you guys turn the exponent 3/2 into 2/3?

wmj259
 one year ago
Best ResponseYou've already chosen the best response.0yes that was a typo on my part, I apologize.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Y'all are fine. I was just making sure.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4\[\large \frac{d}{dx}\left[\frac{2}{3}(\sin(x))^{3/2}\right] = \frac{2}{3} \cdot \frac{3}{2} \cdot (\sin(x))^{(3/2)  1} \cdot \frac{d}{dx} (\sin(x))\]

wmj259
 one year ago
Best ResponseYou've already chosen the best response.0What I would do in this situation would be to first split the problem into 2 different differentiation's because of that subtract sign. You can pull out the (2/3) and the (2/7) because they are constants And then I would do the Power Rule on the (3/2) and the (7/2). Separately. And then I would do the chain rule on the 2 sin(x) functions.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4\[\large \frac{d}{dx}\left[\frac{2}{7}(\sin(x))^{7/2}\right] = \frac{2}{7} \cdot \frac{7}{2} \cdot (\sin(x))^{(7/2)1} \cdot \frac{d}{dx}(\sin(x))\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sin^\frac{ 1 }{ 2 }x*cosx\sin^\frac{ 5 }{ 2 }x*cosx\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4Alright let's check

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I just did the power rule then chain rule as recommended.

wmj259
 one year ago
Best ResponseYou've already chosen the best response.0Is the finished derivative for the left half.

wmj259
 one year ago
Best ResponseYou've already chosen the best response.0the simplified left side is dw:1444351605530:dw

wmj259
 one year ago
Best ResponseYou've already chosen the best response.0Now the right side would give us: dw:1444351641222:dw

wmj259
 one year ago
Best ResponseYou've already chosen the best response.0The simplified right side would be dw:1444351722466:dw

wmj259
 one year ago
Best ResponseYou've already chosen the best response.0So if you combine the left and the right side you get: dw:1444351765027:dw

wmj259
 one year ago
Best ResponseYou've already chosen the best response.0@Catseyeglint911, Which is what you got.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@wmj259 Can you simplify the right side any further?

wmj259
 one year ago
Best ResponseYou've already chosen the best response.0you can say this: dw:1444351917329:dw

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4\[\begin{align}\large \frac{d}{dx}\left[\frac{2}{3}(\sin(x))^{3/2}\right] &= \frac{2}{3} \cdot \frac{3}{2} \cdot (\sin(x))^{(3/2)  1} \cdot \frac{d}{dx} (\sin(x)) \\&= \sin^{1/2}(x)\cos(x) \ \end{align}\]\[\begin{align} \large \frac{d}{dx}\left[\frac{2}{7}(\sin(x))^{7/2}\right] &= \frac{2}{7} \cdot \frac{7}{2} \cdot (\sin(x))^{(7/2)1} \cdot \frac{d}{dx}(\sin(x)) \\&=\sin^{5/2}(x)\cos(x)\end{align}\]\[\begin{align}\frac{d}{dx}\left[ \frac{ 2 }{ 3 }\sin^\frac{ 3 }{ 2 }x\frac{ 2 }{ 7 }\sin^\frac{ 7 }{ 2 }x\right] &= \sin^{1/2}(x)\cos(x) \sin^{5/2}(x)\cos(x) \\&= \sin^{1/2}(x)\cos(x) \left[ 1\sin^{5}(x) \right] \end{align} \]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4\[\large \color{red}{\boxed{\sin^{1/2}(x)\cos(x)\left[1\sin^{5}(x)\right]}}\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4@wmj259 you did something funky heredw:1444352122644:dw

wmj259
 one year ago
Best ResponseYou've already chosen the best response.0Yes, The right most part should have been the derivative of sin(x) not just (x).

wmj259
 one year ago
Best ResponseYou've already chosen the best response.0It goes much longer then that because their is basically a Power rule then 2 chain rules. but the 2nd chain rule is always ignore because its just the derivative of x's in some cases. But with practice comes great speed.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you both! I wish I could give out multiple medals. I'll just become a fan of both of you. :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.