Question

ДАЮ ПРИМЕРНО !)) ПРОИЗВОДНЫЕ

Answer 1

1

$f'(x) = 2 \cos(x) + (3 {x}^{ \frac{4}{5} } ) '- 5 {e}^{x} = \\ = 2 \cos(x) + 3 \times \frac{4}{5} {x}^{ - \frac{1}{5} } - 5 {e}^{x} = \\ = 2 \cos(x) + \frac{12}{5 \sqrt[5]{x} } - 5e {}^{x}$

2

$f'(x) = (4 \times {4}^{x} \times {x}^{4} ) '= ( {4}^{x + 1} \times {x}^{4} ) '= \\ = ( {4}^{x + 1} ) '\times {x}^{4} + ( {x}^{4} ) '\times {4}^{x + 1} = \\ = ln(4) \times {4}^{x + 1} \times {x}^{4} + 4 {x}^{3} \times {4}^{x + 1} = \\ = {4}^{x + 1} \times {x}^{3} ( ln(4) x + 4)$

3

$f'(x) = 3 \times \frac{( ln(x)) ' \times ctgx - (ctgx)' \times ln(x) }{ctg {}^{2}x } = \\ = 3 \times \frac{ \frac{1}{x}ctgx + \frac{1}{ \sin {}^{2} (x) } \times ln(x) }{ {ctg}^{2}x } = \\ = \frac{3}{ {ctg}^{2}x } ( \frac{ctgx}{x} - \frac{ ln(x) }{ \sin {}^{2} (x) } )$