F(x)=(4x^2-7x)^2 f'(0)

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вопрос

To find the derivative of the function f(x) = (4x^2 - 7x)^2 with respect to x, we will use the chain rule and the power rule.

Let u = 4x^2 - 7x. Then, f(x) = u^2.

To find f'(x), we differentiate f(x) with respect to u and then multiply by the derivative of u with respect to x.

f'(u) = 2u
u = 4x^2 - 7x

Now, we differentiate u with respect to x:

du/dx = 8x - 7

Now, we can find f'(x) by multiplying f'(u) and du/dx:

f'(x) = f'(u) du/dx
f'(x) = 2u (8x - 7)

Now, we evaluate f'(0):

f'(0) = 2(0) (8(0) - 7)
f'(0) = 0 (-7)
f'(0) = 0

Therefore, f'(0) = 0.