Calc Deriv/ Is this Correct?

[johnny101]

Hello! I'm trying to figure out if my work/answer is correct on this homework problem. We had a pretty alike problem of calculating the deriv of sqrt(x(x+4)) which gave the answer x+2/ sqrt(x(x+4)), i got that simplification and all. But for this problem below, is my answer correct, or should it be the later simplification?

I have the problem find the derivative of y= sqrt(x(x+5)) assuming dy/dx..the answer I have is x+5/sqrt(x(x+5)), is this correct? Or should it be 2x+5/2(sqrt x(x+5)) ?

 

[srmichael]

Hello! I'm trying to figure out if my work/answer is correct on this homework problem. We had a pretty alike problem of calculating the deriv of sqrt(x(x+4)) which gave the answer x+2/ sqrt(x(x+4)), i got that simplification and all. But for this problem below, is my answer correct, or should it be the later simplification?

I have the problem find the derivative of y= sqrt(x(x+5)) assuming dy/dx..the answer I have is x+5/sqrt(x(x+5)), is this correct? Or should it be 2x+5/2(sqrt x(x+5)) ?

The only reason the first problem became $\displaystyle \dfrac{x+2}{\sqrt{x(x+4)}}$ is because when you took the derivative of x(x+4) you get 2x + 4 which can be factored as 2(x+2) and the 2 on the outside of the parentheses can cancel with the 2 in the denominator that was the result of bringing the exponent down. Thus, for $\displaystyle y=\sqrt{x(x+5)}$ the answer should be.....what?

 

[fcabanski]

Use the chain rule.

The answer is the derivative of what's inside the square root, times the derivative of the square root.

For example, the derivative of sqrt(x^2) = 2x * 1/2(sqrt(x^2)

 

[lookagain]

Use the chain rule.

The answer is the derivative of what's inside the square root, times the derivative of the square root.

For example, the derivative of sqrt(x^2) = 2x * 1/2(sqrt(x^2)

The derivative of $\displaystyle \$ sqrt(x^2) $\displaystyle \$= $\displaystyle \$ 2x * 1/[2*sqrt(x^2)] $\displaystyle \$ = $\displaystyle \$x/sqrt(x^2).