Question

Найдите производную функцию: 1) y=5x^6-cos3x+4^x

2) y=(21x^5+10)^9

3) y=под корнем 4x^7+8

4) y=(sin2x+2cosx)-4^x

Answer 1

1.

$y = 5 {x}^{6} - \cos(3x) + {4}^{x}$

$y' = 5 \times 6 {x}^{5} + \sin(3x) \times (3x)' + {4}^{x} \times ln(4) = \\ = 30 {x}^{5} + 3 \sin(3x) + ln(4) \times {4}^{x}$

2.

$y = {(21 {x}^{5} + 10) }^{9}$

$y' = 9 {(21 {x}^{5} + 10) }^{8} \times (21 {x}^{5} + 10) '= \\ = 9 \times 105 {x}^{4} {(21 {x}^{5} + 10)}^{8} = \\ = 945 {x}^{4} {(21 {x}^{5} + 10) }^{8}$

3.

$y = \sqrt{4 {x}^{7} + 8}$

$y '= \frac{1}{2} {(4 {x}^{7} + 8)}^{ - \frac{1}{2} } \times (4 {x}^{7} + 8) '= \\ = \frac{28 {x}^{6} }{2 \sqrt{4 {x}^{7} + 8} } = \frac{14 {x}^{6} }{ \sqrt{4 {x}^{7} + 8} }$

4.

$y = \sin(2x) + 2 \cos(x) - {4}^{x}$

$y' = 2 \cos(2x) - 2 \sin(x) - {4}^{x} \times ln(4) \\$