Question

^6√x^2+9x помогите решить производную

Answer 1

(6*x+27)/корень(x^2+9*x)

Answer 2

I can help you with finding the derivative of a function. The function you entered is $$\sqrt[6]{x^2+9x}$$

To find the derivative, we can use the chain rule and the power rule. The chain rule says that if $$f(x) = g(h(x))$$, then $$f'(x) = g'(h(x))h'(x)$$.

The power rule says that if $$f(x) = x^n$$, then $$f'(x) = nx^{n-1}$$.

We can rewrite the function as $$f(x) = (x^2+9x)^{1/6}$$ and apply the chain rule. Let $$h(x) = x^2+9x$$ and $$g(x) = x^{1/6}$$. Then we have:

$$f'(x) = g'(h(x))h'(x)$$ $$f'(x) = \frac{1}{6}(x^2+9x)^{-5/6}(2x+9)$$ $$f'(x) = \frac{2x+9}{6\sqrt[6]{(x^2+9x)^5}}$$

This is the derivative of the function. You can learn more about the chain rule and the power rule from these websites: [Symbolab] or [Calculator Online].