Find the derivatives y' . Use the rules

Question

1)y= (square root x)(1+x^2)

2)y= (1/Squareroot x + squareroot x)^2

Answer 1

1) Given that

Differentiate the sum terms by terms and factor out constants

The derivative of 1 is 0

Simplify the expression

The derivative of the given equation is

2) Given that

Differentiate the sum terms by terms and factor out constants

The derivative of the given equation is

Comments

Derivative of √x is 1/(2√x).

Derivative of xⁿ is n*x^{n - 1}.

.

Therefore, .