# How do you differentiate #y=(1+sqrtx)(x^3)# using the product rule?

##### 1 Answer

May 21, 2018

#### Explanation:

#"given "y=g(x)h(x)" then"#

#dy/dx=g(x)h'(x)+h(x)g'(x)larrcolor(blue)"product rule"#

#g(x)=1+sqrtx=1+x^(1/2)#

#rArrg'(x)=1/2x^(-1/2)=1/(2x^(1/2))#

#h)x)=x^3rArrh'(x)=3x^2#

#rArrdy/dx=(1+x^(1/2))3x^2+x^3/(2x^(1/2))#

#color(white)(rArrdy/dx)=3x^2+3x^(5/2)+1/2x^(5/2)#

#color(white)(rArrdy/dx)=3x^2+7/2x^(5/2)#