Derivative of y=x²×3^x?

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Answer 1 · 2018-03-20T09:18:18

#dy/dx = x*3^x(xln3+2)#

#y=x^2*3^x#

#dy/dx = x^2*d/dx(3^x) + d/dx(x^2)*3^x#

Apply standard differential and power rule.

#dy/dx = x^2*ln3*3^x + 2x*3^x#

#= 3^x(x^2ln3+2x)#

#=x*3^x(xln3+2)#