Posted by Anonymous on .
find the derivative of y=[(4^(7x))(7^(4x))]/[10^(e)]
without using logarithmic differentiation!

collge calculus 
drwls,
1/10^e is a constant that you can leave in that form, as a multiplier of the derivative.
Use the product rule for the rest.
For the derivative of 4^7x, let 7x = u
d/dx 4^(7x) = d/du 4^u * d(7x)/dx
= 4^u * ln4 * 7
= 7 ln4 * 4^(7x)
d/dx 7^(4x) = 4 ln7* 7^(4x)
Put it all together