use the PRODUCT RULE when the function that we need to differentiate is actually two functions multiplied together: If  y=uvy=uv  (meaning uu multiplied by vv) then: dydx=udvdx+vdudxdydx=udvdx+vdudx   NOTE:  EXPONENTIAL FUNCTION & Use of BRACKETS

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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We use the PRODUCT RULE when the function that we need to differentiate is actually two functions multiplied together:

If  y=uvy=uv  (meaning uu multiplied by vv) then:

dydx=udvdx+vdudxdydx=udvdx+vdudx

 

NOTE:  EXPONENTIAL FUNCTION & Use of BRACKETS

 

 

 

Differentiate:     y=5x9e4xy=5x9e4x

 

First identify the two functions  uu  and  vv:

u=u=                    v=v=

 

Now differentiate each one:

dudx=dudx=                    dvdx=dvdx=

 

Substitute each component into the formula in the correct place:

dydx=dydx=××++××

 

Finally tidy this up to give your final answer:

dydx=dydx=

 

 

 

 
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