Question

F(x)=(5x+4)^6 Найдите f’(-1)

Answer 1

fx=5x+4

x=-1

(5*-1+4)^6=(-1)^6=1

Answer 2

To find the derivative of the function F(x) = (5x + 4)^6 and then evaluate it at x = -1, we'll use the chain rule of differentiation. The chain rule states that if we have a composite function g(f(x)), then its derivative is given by g'(f(x)) * f'(x). Let's proceed step by step:

Step 1: Find the derivative of the outer function g(u) = u^6 with respect to u. g'(u) = 6u^(6-1) = 6u^5.

Step 2: Find the derivative of the inner function u(x) = 5x + 4 with respect to x. u'(x) = d/dx(5x + 4) = 5.

Step 3: Now, apply the chain rule: F'(x) = g'(u(x)) * u'(x) = 6(5x + 4)^5 * 5.

Step 4: Evaluate F'(-1): F'(-1) = 6(5(-1) + 4)^5 * 5 F'(-1) = 6(-1)^5 * 5 F'(-1) = 6(-1) * 5 F'(-1) = -30.

So, the value of f'(-1) is -30.