Question

Найти производную функции

Answer 1

Відповідь:

Пояснення:

1) y = sqrt(2) * x^4 - x^2/4 + 8

y' = sqrt(2) * 4 * x^3 - x/2 = 4 * sqrt(2) * x^3 - x/2

2) y = 2^(sinx)

y' = 2^(sinx) * ln2 * (sinx)' = ln2 * 2^(sinx) * cosx

3) y = arcsin (e^x / 3)

y' = 1 / sqrt(1 - e^(2x)/9) * (e^x/3)' = e^x / 3sqrt(1 - e^(2x)/9)

4) y = (ln x^3) ^ 2

y' = 2 * (ln x^3) * (ln x^3)' = 2 * (ln x^3) * 1/x^3 * (x^3)' = 2 * (ln x^3) * 3x^2/x^3 = 6x^2lnx^3/x^3

5) y = 3^x e^x

y' = ln3 3^x e^x

6) y = 8x^2 - 16x + sqrt(2)

y' = 16x - 16

7) y = cos(2x - 3) / 2

y' = 1/2 * (-sin(2x - 3)) * (2x - 3)' = -sin(2x - 3)/2 * 2 = -sin(2x - 3)

8) y = x^2 / (3 - x)

y' = 2x * (3-x) - (3-x)' (x^2) / (3 - x)^2 = 6x - 2x^2 + x^2 / (3 - x)^2 = x(6 - x) / (3 - x)^2

9) y = sqrt(x sqrt(x + 7))

y' = 1 / 2sqrt(x sqrt(x + 7)) * (x sqrt(x + 7))' = 1/2sqrt(x sqrt(x + 7)) * (sqrt(x + 7) + x/2sqrt(x+7)) = 1/2sqrt(x sqrt(x + 7)) * ((2x + 14 + x)/2sqrt(x+7)) = 3x + 14/4sqrt(x sqrt(x + 7))sqrt(x+7)

10) y = sin^4(cos4x)

y' = 4sin^3(cos4x) * (-sin4x) * 4 = -16*sin^3(cos4x) * sin4x

Не знаю насколько правильно