February 18th, 2019, 09:20 PM  #1 
Newbie Joined: Feb 2019 From: N/A Posts: 18 Thanks: 0 Math Focus: Calculus  Derivative problems help
Here are some of my practice problems: csc(y^2)=5x+4 and 2x^2+3=e^(2y)^3 Can you show me the steps on each one individually in detail so I can better understand how to do it? 
February 18th, 2019, 09:30 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,530 Thanks: 1390 
are you trying to find $\dfrac{dy}{dx}$ ?

February 18th, 2019, 09:48 PM  #3 
Newbie Joined: Feb 2019 From: N/A Posts: 18 Thanks: 0 Math Focus: Calculus  
February 18th, 2019, 09:58 PM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 2,530 Thanks: 1390  Quote:
$\text{Take derivatives with respect to }x \text{ on boths sides.}$ $\cot(y^2)\csc(y^2)2y y^\prime = 5$ $y^\prime = \dfrac{5}{2y\cot(y^2)\csc(y^2)} = $ $\dfrac{5}{2y} \tan(y^2) \sin(y^2)$  $2x^2+3 = e^{(2y)^3} = e^{8y^3}$ $4x = e^{8y^3}24y^2y^\prime$ $y^\prime = \dfrac{x}{6e^{8y^3}y^2}$  
February 18th, 2019, 10:06 PM  #5  
Newbie Joined: Feb 2019 From: N/A Posts: 18 Thanks: 0 Math Focus: Calculus  Quote:
 

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calculus, derivative, dy/dx, mikeiketube, problems 
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