For example ,
y = 17(22+x)^(41-x)^30
I tried to use math code but it didn't show the exponential numbers/function properly
where the last equality holds because of the chain rule. Now you can apply the product rule (and for the chain rule again) and are done:
P.S: Please note that I have made a silly mistake in my first reply to your question that I have now corrected: the constant factor 17 in front of the power-term can (and should) be left as a factor in front of the remaining exponential mess...
well , It's already written in my book .. when you've said it's a rule I grabbed my book to look for it then I found it under (exponential function to the base of constant ) and compare it to your explanation it was so helpful
and yes the number 17 i knew it was mistake because it's constant and can't be included in derivative thank you for clarifying
you made my calculus life easier
With something like " ", there are two simple mistakes we could make:
1) Treat the exponent, g(x), as a constant and use the "power rule" to get
2) Treat the base, f(x), as a constant and use the "exponential rule" to get " .
The interesting thing is that the correct derivative is the sum of those two errors!
Taking the logarithm of both sides of , . On the left side, . On the right, using the product rule, .
Multiplying on both sides of by , we get