Question #da94a

1 Answer
Øko
Feb 1, 2018

#(x(5x+4))/(2sqrt(x+1))#

Explanation:

We want to find

#(x^2sqrt(x+1))'#

Use the product rule #(f*g)'=f'*g+f*g'#

Let #f=x^2# and #g=sqrt(x+1)#

Then #f'=2x# and #g'=1/(2sqrt(x+1))#

Therefore the derivative is

#2x*sqrt(x+1)+x^2*1/(2sqrt(1+x))#

Or simplified

#(x(5x+4))/(2sqrt(x+1))#

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