Question

Найти производную: 1) у=7x^7+3x^2-4x-1 2) y=x /4x 3) y= x^3 + 2x / e^x 4) y= lnx / 1+x^2

Answer 1

1) $y = 7x^7+3x^2-4x-1$

$y' = 49x^6+6x-4$ 

2) $y = \frac{x}{4x} = 1/4$ 

$y' = 0$ 

3) $y = x^3 + \frac{2x}{e^x}$ 

$y' = 3x^2+\frac{2e^x-2xe^x}{e^{2x}} = 3x^2+2\frac{1-x}{e^x}$ 

4) $y = \frac{lnx}{1+x^2}$ 

$y' = \frac{\frac{1}{x}(1+x^2)-2xlnx}{(1+x^2)^2} = \frac{x^2(1-2lnx)+1}{x(1+x^2)^2}$