Question

Найдите производную при данном значения аргументаF(x)=(xстепень2+4x+2)степень4;x=1

Answer 1

F ' (x) = 4 (x^2  + 4x + 2)^3 (x^2 + 4x + 2) ' =
= 4 (2x + 4) (x^2 + 4x + 2)^3 

f ' (1) = 4*6*343 = 8 232

Answer 2

Derivative of the Function at a Given Value

To find the derivative of the function \( F(x) = (x^2 + 4x + 2)^4 \) at \( x = 1 \), we can use the power rule and chain rule of differentiation.

Solution

The derivative of the function \( F(x) = (x^2 + 4x + 2)^4 \) with respect to \( x \) is given by:

\[ F'(x) = 4(x^2 + 4x + 2)^3 \cdot (2x + 4) \]

Now, to find the value of the derivative at \( x = 1 \), we substitute \( x = 1 \) into the derivative function:

\[ F'(1) = 4(1^2 + 4 \cdot 1 + 2)^3 \cdot (2 \cdot 1 + 4) \]

\[ F'(1) = 4(1 + 4 + 2)^3 \cdot (2 + 4) \]

\[ F'(1) = 4(7)^3 \cdot 6 \]

\[ F'(1) = 4 \cdot 343 \cdot 6 \]

\[ F'(1) = 8232 \]

Answer

So, the value of the derivative of the function \( F(x) = (x^2 + 4x + 2)^4 \) at \( x = 1 \) is 8232.