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
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
Section: Chapter Questions
Problem 1RQ
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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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