August 6th, 2012, 12:27 PM  #1 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  differentiation of the form b^ax
hello i'm new to the concept of differentiation (dy/dx) and i read y=e^ax should become a*e^ax (for example e^3x > 3*e^3x) but then i was stuck when i had something like y=7^3x; or something like y=b^ax so i thought lets transfer b^a to like e^A by doing this i got ln(b^a)*e^ln(b^a)x z=e^A ln(z)=A b^ax > A*e^Ax b^ax > ln(z)*e^ln(z)x b^ax > ln(b^a)*e^ln(b^a)x could someone tell me if this is correct or if there would be an better way to get this ? 
August 6th, 2012, 12:49 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: differentiation of the form b^ax
One way to differentiate: where a and b are constants is to take the natural log of both sides: Now, implicitly differentiate with respect to x: Your result is equivalent after simplification. 
August 6th, 2012, 07:54 PM  #3 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: differentiation of the form b^ax
Another equivalent method but we don't have to differentiate logarithmic function this time: It is known that ; use chain rule: QED and we completely avoided logarithmic differentiation. Balarka . 
August 6th, 2012, 08:01 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: differentiation of the form b^ax
Is exponential differentiation somehow to be preferred over logarithmic differentiation? 
August 6th, 2012, 08:16 PM  #5  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: differentiation of the form b^ax Quote:
Balarka .  
August 6th, 2012, 08:20 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: differentiation of the form b^ax Ah...I understand! 

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