Question #0fea1

1 Answer
Cesareo R.
Mar 28, 2017

#(dy)/(dx)=((x^2-2)^2 (x (70 + x (173 + 37 x))-22))/(3 (4 + x)^(4/3) sqrt[1 + 2 x])#

Explanation:

#y=f_1(x)f_2(x)f_3(x)# so

#(dy)/(dx)=(df_1)/(dx)f_2 f_3+f_1((df_2)/(dx))f_3+f_1f_2((df_3)/(dx))#

#f_1=sqrt(2x+1)# so #(df_1)/(dx)=1/2 2/sqrt(2x+1)#
#f_2=(x^2-2)^3# so #(df_2)/(dx)=3 xx 2 x(x^2-2)^2#
#f_3=1/root(3)(x+4)#so #(df_3)/(dx)=-1/3 1/root(4/3)(x+4)#

Putting all together

#(dy)/(dx)=(6 x sqrt[1 + 2 x] (x^2-2)^2)/(4 + x)^( 1/3) + (x^2-2)^3/((4 + x)^(1/3) sqrt[1 + 2 x]) - ( sqrt[1 + 2 x] (x^2-2)^3)/(3 (4 + x)^(4/3))#

or

#(dy)/(dx)=((x^2-2)^2 (x (70 + x (173 + 37 x))-22))/(3 (4 + x)^(4/3) sqrt[1 + 2 x])#

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