# How do you differentiate #y=(5x^5+5)(-2x^5-3)# using the product rule?

##### 1 Answer

Mar 11, 2017

#### Explanation:

#"Given " y=g(x).h(x)" then"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(dy/dx=g(x)h'(x)+h(x)g'(x))color(white)(2/2)|)))larr" product rule"#

#"here " g(x)=5x^5+5rArrg'(x)=25x^4#

#"and " h(x)=-2x^5-3rArrh'(x)=-10x^4#

#rArrdy/dx=(5x^5+5)(-10x^4)+(-2x^5-3)(25x^4)#

#color(white)(rArrdy/dx)=-50x^9-50x^4-50x^9-75x^4#

#color(white)(rArrdy/dx)=-100x^9-125x^4#