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Differentiate and Simplify:

 

Find dy/dx: y = x7(2x+5)10

 

Please explain how you would solve this

Guest Sep 15, 2017
edited by Guest  Sep 15, 2017
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2+0 Answers

 #1
avatar+78577 
+1

 

y = (x)^7 * (2x + 5)^10

 

We want to use the product and chain rules, here...remember that if

 

y = u * v  ......then   y'  =  u' * v + u * v'       where u, v are functions....so we have.....

 

dy / dx  =   7(x)^6 * (2x + 5)^10  + (x)^7 * 10 * (2x + 5)^9 *(2) 

 

Note that we used the chain rule  in the last part [ in red ]

 

We can simplify thus.....factor out GCF of [ x^6 * ( 2x + 5)^9]

 

[ x^6 * ( 2x + 5)^9] * [  7 (2x + 5)  +  20x ]  

 

[ x^6 * ( 2x + 5)^9] * [ 14x  + 35 + 20x ] 

 

[x^6 * (2x + 5)^9 ] * [ 34x + 35 ] 

 

 

cool cool cool

CPhill  Sep 15, 2017
 #2
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0

-3( 2x + 5 )=-21 

 

pls answer tq

Guest Sep 15, 2017

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