How do you differentiate #y=(-7x^4+10x^(2/5)+8)(x^2+10)# using the product rule?

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How do you differentiate #y=(-7x^4+10x^(2/5)+8)(x^2+10)# using the product rule?

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Answer 1 · 2017-10-05T19:19:39

#(dy)/(dx)=(-7x^4+10x^(2/5)+8)2x+(x^2+10)(-28x^3+4x^(-3/5))#

Explanation:

Solve by using the product rule.
#(dy)/(dx)=f(x)g'(x)+g(x)f'(x)#

#f(x)=-7x^4+10x^(2/5)+8#
#g(x)=x^2+10#
#f'(x)=28x^3+4x^(-3/5)#
#g'(x)=2x#

#(dy)/(dx)=(-7x^4+10x^(2/5)+8)2x+(x^2+10)(-28x^3+4x^(-3/5))#

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How do you differentiate #y=(-7x^4+10x^(2/5)+8)(x^2+10)# using the product rule?

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