What is the derivative of # e^(x^3)+log_5(pi)#?

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Answer 1 · 2018-03-03T09:36:44

#d/dx e^(x^3) + log_5(pi) = 3x^2e^(x^3) #

The #log_5 (pi)# is a constant, so the derivative of the function can be turned down to a simpler #d/dx e^(x^3)#.

Let #y# be equal to #e^(x^3)#. Take the natural logarithm of both sides.

#ln y = x^3 *ln e#
#ln y= x^3#

Differentiate both :

#dy/dx 1/y = 3x^2#

#dy/dx = y*3x^2 = 3x^2e^(x^3)#, so

#color(blue)(d/dx e^(x^3) + log_5(pi) = 3x^2e^(x^3))#.