Differentiate? #F(y) = (1/y^2 - 5/y^4) (y +7y^3) #

1 Answer
May 12, 2017

Answer:

#(dF(y))/dy = (-2y^-3+20y^-5)(y+7y^3)+(1/y^2-5/y^4)(1+21y^2)#

Explanation:

Use the product rule:

#(dF(y))/dy = (d(1/y^2-5/y^4))/dy(y+7y^3)+(1/y^2-5/y^4)(d(y+7y^3))/dy#

Do the first derivative:

#(d(1/y^2-5/y^4))/dy=(d(y^-2-5y^-4))/dy =-2y^-3+20y^-5#

Substitute back into the product rule:

#(dF(y))/dy = (-2y^-3+20y^-5)(y+7y^3)+(1/y^2-5/y^4)(d(y+7y^3))/dy#

Do the second derivative:

#(d(y+7y^3))/dy = 1+21y^2#

Substitute back into the product rule:

#(dF(y))/dy = (-2y^-3+20y^-5)(y+7y^3)+(1/y^2-5/y^4)(1+21y^2)#