Question

Y= кореньx^2 +7, y'-?​

Answer 1

Решение во вложении:

Answer 2

To find the derivative of the function $y = \sqrt{x^2 + 7}$ with respect to $x$, we can use the chain rule.

The chain rule states that if we have a function $y = g(f(x))$, then the derivative of $y$ with respect to $x$ is given by $\frac{{dy}}{{dx}} = \frac{{dy}}{{df}} \cdot \frac{{df}}{{dx}}$.

In this case, $g(u) = \sqrt{u}$ and $f(x) = x^2 + 7$.

Let's find the derivatives step-by-step:

1. $\frac{{df}}{{dx}}$: The derivative of $x^2 + 7$ with respect to $x$ is simply $2x$.

2. $\frac{{dy}}{{df}}$: The derivative of $\sqrt{u}$ with respect to $u$ is $\frac{1}{2\sqrt{u}}$.

Now, using the chain rule:

$\frac{{dy}}{{dx}} = \frac{{dy}}{{df}} \cdot \frac{{df}}{{dx}}$ $\frac{{dy}}{{dx}} = \frac{1}{{2\sqrt{x^2 + 7}}} \cdot 2x$

Simplifying:

$\frac{{dy}}{{dx}} = \frac{x}{{\sqrt{x^2 + 7}}}$

So, the derivative of $y = \sqrt{x^2 + 7}$ with respect to $x$ is $\frac{x}{{\sqrt{x^2 + 7}}}$.