Question

ребят помогите пожалуйста решить 

Answer 1

1. у = 5x³ - 3x + 7
y' = 15x² -3

2. y = ctg x·(2x³ + 5x)
y' = - $frac{2x^{3} + 5x}{sin^{2}x }$ + ctg x·(6x² + 5)

3. y = $frac{ e^{x}}{3x^{4}-2x}$
y' = $frac{ e^{x}(3x^{4}-2x)-e^{x}(12x^{3}-2)}{(3x^{4}-2x)^{2}}=frac{ e^{x}(3x^{4}-12x^{3}-2x+2)}{(3x^{4}-2x)^{2}}$

4. y = log₃(4x⁵ - 3x²)
y' = $frac{20x^{4}-6x}{ln3(4x^{5}-3x^{2})}= frac{2(10x^{3}-3)}{ln3(4x^{4}-3x)}$

5. y = -2cos(2x⁵ - 6x)
y' = 2sin(2x⁵ - 6x)·(10x⁴ - 6) = 4·(5x⁴ - 3)·sin(2x⁵ - 6x)

6. y = $sqrt{4x^{3}+2}$
$y'= frac{12 x^{2} }{2 sqrt{4x^{3}+2}} = frac{6 x^{2} }{sqrt{4x^{3}+2}}$