Questions: Find y''. y = sqrt(7x+10) A. 7 / (2 sqrt(7x+10)) B. -49 / (4(7x+10)^(3/2)) C. -1 / (4(7x+10)^(3/2)) D. -49 sqrt(7x+10) / 4

Solution Steps

To find the second derivative \( y'' \) of the function \( y = \sqrt{7x + 10} \), we need to follow these steps:

1. Find the first derivative \( y' \) using the chain rule.
2. Find the second derivative \( y'' \) by differentiating \( y' \) again.

To find the first derivative of the function \( y = \sqrt{7x + 10} \), we apply the chain rule: \[ y' = \frac{d}{dx}(\sqrt{7x + 10}) = \frac{7}{2\sqrt{7x + 10}} \]

Next, we differentiate \( y' \) to find the second derivative \( y'' \): \[ y'' = \frac{d}{dx}\left(\frac{7}{2\sqrt{7x + 10}}\right) = -\frac{49}{4(7x + 10)^{3/2}} \]

Final Answer