How do you find the tangent line approximation for #f(x)=sqrt(1+x)# near #x=0# ? Calculus Applications of Derivatives Using the Tangent Line to Approximate Function Values 1 Answer AJ Speller Sep 24, 2014 We need to find the derivative of #f(x)#. We need to use the Chain Rule to find the derivative of #f(x)#. #f(x)=sqrt(1+x)=(1+x)^(1/2)# #f'(x)=(1/2)(1+x)^((1/2-1))*1# #f'(x)=(1/2)(1+x)^((1/2-2/2))# #f'(x)=(1/2)(1+x)^((-1/2))# #f'(x)=1/(2sqrt(1+x))# #f'(0)=1/(2sqrt(1+0))=1/(2sqrt(1))=1/2=0.5# Answer link Related questions How do you find the linear approximation of #(1.999)^4# ? How do you find the linear approximation of a function? How do you find the linear approximation of #f(x)=ln(x)# at #x=1# ? How do you find the tangent line approximation to #f(x)=1/x# near #x=1# ? How do you find the tangent line approximation to #f(x)=cos(x)# at #x=pi/4# ? How do you find the tangent line approximation to #f(x)=e^x# near #x=0# ? How do you use the tangent line approximation to approximate the value of #ln(1003)# ? How do you use the tangent line approximation to approximate the value of #ln(1.006)# ? How do you use the tangent line approximation to approximate the value of #ln(1004)# ? What is the linear approximation of a function? See all questions in Using the Tangent Line to Approximate Function Values Impact of this question 19246 views around the world You can reuse this answer Creative Commons License