Question

Решите пожалуйста,срочно нужно)) 1)f(x)=(x^3-x^5+6)^7 2)f(x)=(5-3x^3+x^4)^6 3)f(x)=(3√x+2x)^5 4)f(x)=(8√x+4x^2)^8

Answer 1

Производная функции вида  $f(x)=u(x)^n$ считается по такой формуле:
$f'(x)=n*u(x)^{n-1}*u'(x)$

1)  $f'(x)=7(x^3-x^5+6)^6*(3x^2-5x^4)$
2)  $f'(x)=6(5-3x^3+x^4)^5*(-9x^2+4x^3)$
3)  $f'(x)=5(3 \sqrt{x} +2x)^4*( \frac{3}{2 \sqrt{x} } +2)$
4)  $f'(x)=8(8 \sqrt{x} +4x^2)^7*( \frac{4}{ \sqrt{x} } +8x)$

Answer 2

1. f(x) = (x^3 - x^5 + 6)^7 There is no specific question mentioned here. Assuming you need to find the derivative of the given function, we can use the chain rule and the power rule of differentiation to get:

f'(x) = 7(x^3 - x^5 + 6)^6 (3x^2 - 5x^4)

2. f(x) = (5 - 3x^3 + x^4)^6 Again, assuming you need to find the derivative of the given function, we can use the chain rule and the power rule of differentiation to get:

f'(x) = 6(5 - 3x^3 + x^4)^5 (-9x^2 + 4x^3)

3. f(x) = (3√x + 2x)^5 Using the chain rule and power rule of differentiation, we get:

f'(x) = 5(3√x + 2x)^4 * (3/2x^(-1/2) + 2) Simplifying this expression, we get:

f'(x) = 15(3√x + 2x)^4/x^(1/2) + 10(3√x + 2x)^4

4. f(x) = (8√x + 4x^2)^8 Using the chain rule and power rule of differentiation, we get:

f'(x) = 8(8√x + 4x^2)^7 (4/x^(1/2) + 8x) Simplifying this expression, we get:

f'(x) = 32(8√x + 4x^2)^7/x^(1/2) + 64x(8√x + 4x^2)^7

Note: These are just the derivatives of the given functions. If you have any specific question or requirement, please let me know, and I will be happy to assist you further.