Question

Y=(2x-5)^6Вычислите производную​

Answer 1

$y'=((2x-5)^6)'=6(2x-5)^5\cdot(2x-5)'=6(2x-5)^5\cdot2=12(2x-5)^5$

Answer 2

To find the derivative of the function Y = (2x - 5)^6 with respect to x, you can use the chain rule. The chain rule states that if you have a composition of functions, such as (f(g(x)))^n, then the derivative is given by n * (f(g(x)))^(n-1) * f'(g(x)) * g'(x).

Let's apply the chain rule step by step:

Step 1: Identify the outer function and the inner function. Outer function: u^n, where u = (2x - 5) and n = 6. Inner function: u = 2x - 5.

Step 2: Find the derivative of the outer function. d/du (u^n) = n * u^(n-1) = 6 * (2x - 5)^(6-1) = 6 * (2x - 5)^5.

Step 3: Find the derivative of the inner function. d/dx (2x - 5) = 2.

Step 4: Apply the chain rule. dY/dx = (d/du(u^n)) * (d/dx(2x - 5)) = 6 * (2x - 5)^5 * 2 = 12 * (2x - 5)^5.

So, the derivative of the function Y = (2x - 5)^6 with respect to x is 12 * (2x - 5)^5.