differentiate using chain rule

Question

differentiate

g(x)=((2x^3+1)/(x^2+1))^(-2/3)

f(x)=e^(tan(sqrt x)+1)

Answer 1

Step 1:

The function is .

Apply derivative on each side with respect to .

Use power rule combined  with the chain rule of derivative : .

Step 2:

The function is .

Apply derivative on each side with respect to .

Use exponential rule combined with chain rule of derivative : .

Solution :