find the first derivative
y= 2/5square root2x+1
To find the first derivative of the function y = (2/5)√(2x + 1), you can use the power rule and chain rule.
Step 1: Rewrite the function using exponent notation.
y = (2/5)(2x + 1)^(1/2)
Step 2: Apply the power rule by multiplying the coefficient of the function by the exponent and subtracting 1 from the exponent.
y' = (2/5) * (1/2)(2x + 1)^(-1/2)
Step 3: Simplify the expression.
y' = (1/5)√(2x + 1)^(-1/2)
= √(2x + 1)/(5√(2x + 1))
= 1/(5√(2x + 1))
So, the first derivative of y = (2/5)√(2x + 1) is y' = 1/(5√(2x + 1)).