Question

Найти y'(-1) если y=(2x+3)^6

Answer 1

Ответ: 12.

Дано: y = (2*x+3)⁶,

Xo = - 1

Найти: y'(Xo) = ?

Пошаговое объяснение:

y'(x) =  6*(2x+3)⁵ *2 = 12*(2*x+3)⁵

y'(-1) = 12*(-2+3)⁵ = 12 - ответ.

Answer 2

To find the derivative of y, we can use the chain rule. Let u = 2x + 3, then y = u^6.

Using the chain rule, we have:

y' = 6u^5 * u'

To find y'(-1), we need to evaluate y' when x = -1.

Since u = 2x + 3, when x = -1, we have u = 2(-1) + 3 = 1.

Also, u' = 2, since the derivative of 2x + 3 is 2.

Substituting these values into our expression for y', we get:

y'(-1) = 6(1)^5 * 2 = 12

Therefore, y'(-1) = 12.