The answer is: #h'(x)=(2x+7)^3(x-1)(14x^2+11x-7)#.
#h'(-3)=344#
Rememering that:
#y=f(x)*g(x)rArry'=f'(x)*g(x)+f(x)g'(x)#
Since:
#h(x)=x(2x+7)^4(x-1)^2#
than:
#h'(x)=1*(2x+7)^4*(x-1)^2+x*4(2x+7)^3*2*(x-1)^2+x(2x+7)^4*2(x-1)^1*1=#
#=(2x+7)^3(x-1)*[(2x+7)(x-1)+8x(x-1)+2x(2x+7)]=#
#=(2x+7)^3(x-1)*(2x^2-2x+7x-7+8x^2-8x+4x^2+14x)=#
#=(2x+7)^3(x-1)(14x^2+11x-7)#.
#h'(-3)=(2*(-3)+7)^3(-3-1)(14*(-3)^2+11*(-3)-7)=#
#=(1)^3(-4)(86)=344#