Найти производную функции помогите, пожалуйста 40 балл.

Question 1

Найти производную функции
помогите, пожалуйста 40 балл.

Question 2

1. (3x² - 1/x³) ' = (3x²) ' - (1/x³) ' = 6x - (x⁻³)' = 6x + 3x⁻⁴ = 6x + 3/x⁴

2. ((x/3 + 7)⁶) ' = 6(x/3 + 7)⁵ · (x/3 + 7)' = 6(x/3 + 7)⁵ · 1/3 = 2(x/3 +7)⁵

3. (eˣ·cosx) ' = (eˣ)' · cosx + eˣ · (cosx)' = eˣ · cosx + eˣ · (- sinx) = eˣ(cosx - sinx)

4. (2ˣ / sinx) ' = $\frac{ (2^{x})'sinx - 2^{x}(sinx)' }{ sin^{2}x } = \frac{ 2^{x}ln2 sinx - 2^{x}cosx }{ sin^{2}x }$

5. (2x³ - 1/x²)' = (2x³) ' - (x⁻²)' = 6x² + 2x⁻³ = 6x² + 2/x³

6. ((x/7 + 13)⁸) ' = 8(x/7 + 13)⁷ · (x/7 + 13)' = 8(x/7 + 13)⁷ · 1/7 = 8/7 (x/7 + 13)⁷

7. (eˣsinx) ' = (eˣ) ' sinx + eˣ (sinx) ' = eˣ sinx + eˣ cosx

8. (3ˣ / cosx) ' = $\frac{ (3^{x})'cosx - 3^{x}(cosx)' }{ cos^{2}x } = \frac{ 3^{x} ln3 cosx + 3^{x} sinx }{ cos^{2}x }$

KuOV_zn · Answer 1 · 2018-05-16T15:23:11+0000

1. (3x² - 1/x³) ' = (3x²) ' - (1/x³) ' = 6x - (x⁻³)' = 6x + 3x⁻⁴ = 6x + 3/x⁴

2. ((x/3 + 7)⁶) ' = 6(x/3 + 7)⁵ · (x/3 + 7)' = 6(x/3 + 7)⁵ · 1/3 = 2(x/3 +7)⁵

3. (eˣ·cosx) ' = (eˣ)' · cosx + eˣ · (cosx)' = eˣ · cosx + eˣ · (- sinx) = eˣ(cosx - sinx)

4. (2ˣ / sinx) ' = $\frac{ (2^{x})'sinx - 2^{x}(sinx)' }{ sin^{2}x } = \frac{ 2^{x}ln2 sinx - 2^{x}cosx }{ sin^{2}x }$

5. (2x³ - 1/x²)' = (2x³) ' - (x⁻²)' = 6x² + 2x⁻³ = 6x² + 2/x³

6. ((x/7 + 13)⁸) ' = 8(x/7 + 13)⁷ · (x/7 + 13)' = 8(x/7 + 13)⁷ · 1/7 = 8/7 (x/7 + 13)⁷

7. (eˣsinx) ' = (eˣ) ' sinx + eˣ (sinx) ' = eˣ sinx + eˣ cosx

8. (3ˣ / cosx) ' = $\frac{ (3^{x})'cosx - 3^{x}(cosx)' }{ cos^{2}x } = \frac{ 3^{x} ln3 cosx + 3^{x} sinx }{ cos^{2}x }$