How do you find the derivative of #x^3(2x-5)^4#?
1 Answer
Jan 29, 2016
Explanation:
Differentiate using the
# color(blue)(" product and chain rule")# Product rule:
#d/dx ( f(x).g(x)) = f(x).g'(x) + g(x).f'(x)#
# d/dx (x^3(2x-5)^4 )#
# = x^3 d/dx(2x-5)^4+ (2x-5)^4 d/dx (x^3) #
# = x^3[4(2x-5)^3 d/dx(2x-5)] + (2x-5)^4 .3x^2 #
# = x^3[4(2x-5)^3 .2] + 3x^2(2x-5)^4 #
# = 8x^3(2x-5)^3 + 3x^2(2x-5)^4 #
# = x^2(2x-5)^3[ 8x+ 3(2x-5)]#
# = x^2(2x-5)^3(14x - 15) #
