nameVoid said:D= (x^2+x)^(1/2)
I have a solutions manual here showing
D' = (1/2)(x^2+x)^(-1/2) (2x+1)(x')
but correct me if I am wrong..
D' = (1/2)(x^2+x)^(-1/2) (2x+1)(2x')
The derivative of (x^2+x)^(1/2) is (2x+1)/(2√(x^2+x)).
Yes, there is a simple solution manual. It involves using the power rule, chain rule, and quotient rule.
First, rewrite the function as (x^2+x)^0.5. Then, use the power rule to bring down the exponent, resulting in 0.5(x^2+x)^-0.5. Next, apply the chain rule by multiplying by the derivative of the inside function, which is 2x+1. Finally, use the quotient rule to divide by the original function, resulting in the final derivative of (2x+1)/(2√(x^2+x)).
The derivative of a function represents the rate of change of the function at a specific point. It can also be interpreted as the slope of the tangent line at that point. This information is useful in many applications, such as determining maximum and minimum values, optimization problems, and graphing functions.
Yes, the derivative of (x^2+x)^(1/2) can be used in physics for calculating the velocity and acceleration of an object in motion. It can also be used in economics for analyzing marginal cost and revenue. Additionally, it can be used in engineering for designing curved structures and calculating fluid flow rates.