How do you differentiate #t(x)= 3^(7x-3)#?

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Answer 1 · 2016-11-20T15:07:10

Take the natural logarithm of each side.

#y = 3^(7x - 3)#

#lny = ln(3^(7x- 3))#

#lny = (7x - 3)ln3#

Differentiate using the product rule and the rule that #(lnx)' = 1/x#.

#1/y(dy/dx) = 7ln3 + (7x - 3)0#

#1/y(dy/dx) = 7ln3#

#dy/dx = 7ln3/(1/y)#

#dy/dx= yln3^7#

#dy/dx= 3^(7x- 3)ln2187#

Hopefully this helps!