Prove that the derivative of #(e^(4x)/4-xe^(4x) ) = pxe^(4x) # and find #p#?
1 Answer
Sep 25, 2017
Explanation:
Differentiating wrt
# d/dx (e^(4x)/4-xe^(4x) ) = d/dx (e^(4x)/4) - x(d/dx e^(4x) ) - (d/dx x)(e^(4x) ) #
# " " = d/dx ((4e^(4x))/4) - x(4e^(4x) ) - (1)(e^(4x) ) #
# " " = e^(4x) - 4xe^(4x) - e^(4x ) #
# " " = - 4xe^(4x) #
# " " = pxe^(4x) # , where#p=-4#