Question

F(x)=(3x-5)^4. f'(1)=?

Answer 1

F(x)=(3x-5)^4
F'(x)=4*3*(3x-5)^3=12*(3x-5)^3
F'(1)=12*(3*1-5)^3=12*(-2)^3=-12*8=-96
Ответ : -96

Answer 2

F'(x)= 4*(3x-5)^3 *(3x-5)' = 4*(3x-5)^3 *3 = 12*(3x-5)^3

f'(1)= 12*(3*1-5)^3= 12*(-2)^3=12*(-8) = -96

Answer 3

To find the derivative of the function f(x) = (3x - 5)^4 and evaluate it at x = 1, we can use the chain rule. The chain rule states that if we have a composite function, such as f(g(x)), the derivative is given by the derivative of the outer function multiplied by the derivative of the inner function.

Let's calculate the derivative step by step:

1. Apply the chain rule: f'(x) = 4(3x - 5)^3 * (d/dx)(3x - 5). The derivative of the outer function (3x - 5)^4 is 4(3x - 5)^3. Now we need to find the derivative of the inner function, (3x - 5).

2. Calculate the derivative of (3x - 5): d/dx (3x - 5) = 3. The derivative of 3x with respect to x is 3, and the derivative of a constant (-5) is 0.

3. Substitute the derivative of (3x - 5) back into the expression for f'(x): f'(x) = 4(3x - 5)^3 * 3.

4. Evaluate f'(x) at x = 1: f'(1) = 4(3(1) - 5)^3 * 3 = 4(-2)^3 * 3 = 4(-8) * 3 = -32 * 3 = -96.

Therefore, f'(1) = -96.