Differentiation

[whiteti]

Find the derivative of the function using the rules of differentiation:

y=x^5cotx

Alright so I'm pretty sure this is the chain rule, and i know the derivative of cotx = csc^2x. Im struggling with putting the rules together. Please help

 

[srmichael]

Find the derivative of the function using the rules of differentiation:

y=x^5cotx

Alright so I'm pretty sure this is the chain rule, and i know the derivative of cotx = csc^2x. Im struggling with putting the rules together. Please help

First, the derivative of cot(x) is not csc²(x). It is -csc²(x).

That being said, the chain rule says \(\displaystyle \frac{d}{dx}(u \cdot v)=\frac{d}{dx}(u) \cdot v + u \cdot \frac{d}{dx}(v)\) where U and v are functions of x. So in your equation, let u = x^5 and v = cot(x) and then apply the rule. Take a shot and let us know what you get.

 

[Deleted member 4993]

Find the derivative of the function using the rules of differentiation:

y=x^5cotx

Alright so I'm pretty sure this is the chain rule, and i know the derivative of cotx = csc^2x. Im struggling with putting the rules together. Please help

Is it

\(\displaystyle y \ = \ x^5 \ * \ cot(x)\)

or

\(\displaystyle y \ = \ x^{5cot(x)}\)

 

[whiteti]

Is it

\(\displaystyle y \ = \ x^5 \ * \ cot(x)\)

or

\(\displaystyle y \ = \ x^{5cot(x)}\)

it is multiplied by

 

[whiteti]

so now im at

y= (5x^4)(cotx) + (x^5)(-csc^2x)

is this what I should have so far?

 

[srmichael]

it is multiplied by

Cool. Then proceed with what I stated above and show us what you get.

 

[srmichael]

so now im at

y= (5x^4)(cotx) + (x^5)(-csc^2x)

is this what I should have so far?

YUP! You can always simplify a bit by factoring out an x^4, but that is correct, nonetheless!

 

[mmm4444bot]

it is multiplied by

C'mon! What are you trying to say, by posting that phrase?

 

[whiteti]

C'mon! What are you trying to say, by posting that phrase?

sorry it is: [FONT=MathJax_Math]y[/FONT][FONT=MathJax_Main] [/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main] [/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]5[/FONT][FONT=MathJax_Main] [/FONT][FONT=MathJax_Main]∗[/FONT][FONT=MathJax_Main] [/FONT][FONT=MathJax_Math]c[/FONT][FONT=MathJax_Math]o[/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT]

 

[whiteti]

Thanks!!