How do you find the derivative of #x*sqrt(x+1)#?

1 Answer
Jun 3, 2016

Answer:

#d/(d x)(x*sqrt(x+1))=(3x+2)/(2*sqrt(x+1))#

Explanation:

#d/(d x)(x*sqrt(x+1))=?#

#d/(d x)(x*sqrt(x+1))=x^'*sqrt(x+1)+(sqrt(x+1))^'*x#

#d/(d x)(x*sqrt(x+1))=1*sqrt(x+1)+1/(2*sqrt(x+1))*x#

#d/(d x)(x*sqrt(x+1))=sqrt(x+1)+x/(2*sqrt(x+1))#

#d/(d x)(x*sqrt(x+1))=[(2*sqrt(x+1)*sqrt(x+1))+x]/(2*sqrt(x+1))#

#d/(d x)(x*sqrt(x+1))=(2x+2+x)/(2*sqrt(x+1))#

#d/(d x)(x*sqrt(x+1))=(3x+2)/(2*sqrt(x+1))#