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

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

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

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

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

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