How do you use the Product Rule to find the derivative of #y = (x^2 + 6) (4x^6 + 5) #?

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Answer 1 · 2015-08-16T19:22:19

#color(red)(dy/dx=24x^5(x^2+6) +2x(4x^6+5))#

The Product Rule, states that if #y=uv#, then

#dy/dx = u(dv)/dx+v(du)/dx#

Let #u=x^2+6# and #v=4x^6+5#

Then

#(du)/dx=2x#

#(dv)/dx=24x^5#

#dy/dx = u(dv)/dx+v(du)/dx#

#dy/dx=(x^2+6)× 24x^5 +(4x^6+5)×2x#

#dy/dx=24x^5(x^2+6) +2x(4x^6+5)#