Question

Найти производную y=(+7)⁷

Answer 1

$y' = 7(\frac{x}{3} +7)^6*(\frac{x}{3} +7)' = \frac{7}{3} (\frac{x}{3} +7)^6$

Answer 2

To find the derivative of the function y = (+7)⁷, I assume you meant y = (x + 7)⁷, where x is the independent variable. Let's proceed with the differentiation using the chain rule.

The chain rule states that if we have a function of the form u = g(x)ⁿ, then its derivative with respect to x, du/dx, is given by du/dx = n * g(x)^(n-1) * g'(x), where g'(x) is the derivative of g(x) with respect to x.

In our case, u = (x + 7)⁷, so we'll apply the chain rule:

Step 1: Identify g(x) and n. g(x) = x + 7 n = 7

Step 2: Find g'(x). The derivative of g(x) with respect to x is the derivative of x + 7, which is simply 1.

Step 3: Apply the chain rule formula. dy/dx = 7 * (x + 7)^(7-1) * 1

Simplifying: dy/dx = 7 * (x + 7)⁶

So, the derivative of y = (x + 7)⁷ with respect to x is dy/dx = 7 * (x + 7)⁶.