ПроизводноеЧастного.1)F(x)=15x+3/3x^2-12)F(x)=2√x-100/3√x3)F(x)=(2√x+5)×√x^3 4)F(x)=...

1) $f'(x)=\frac{(15x+3)'*(3x^{2}-1)-(15x+3)(3x^{2}-1)'}{(3x^{2}-1)^{2}}= \frac{15*(3x^{2}-1)-6x*(15x+3)}{(3x^{2}-1)^{2}}=$ $\frac{45x^{2}-15-90x^{2}-18x}{(3x^{2}-1)^{2}}=\frac{-45x^{2}-18x-15}{(3x^{2}-1)^{2}}=\frac{-3*(15x^{2}+6x+5)}{(3x^{2}-1)^{2}}$

2) $f'(x)=\frac{(2\sqrt{x}-100)'*(3\sqrt{x})-(2\sqrt{x}-100)*(3\sqrt{x})'}{(3\sqrt{x})^{2}}=$ $\frac{2*0.5*x^{-0.5}*3*x^{0.5}-3*0.5*x^{-0.5}*2x^{0.5}+3*0.5*x^{-0.5}*100}{9x}=\frac{3-3+150*x^{-0.5}}{9x}=\frac{50}{3x\sqrt{x}}=$ $\frac{50\sqrt{x}}{3x^{2}}$

3) $f(x)=(2 \sqrt{x}+5)*\sqrt{x^{3}}=2x^{0.5+1.5}+5x^{1.5}=2x^{2}+5x^{1.5}$
$f'(x)=(2x^{2}+5x^{1.5})'=2*2*x+5*1.5*x^{0.5}=4x+2.5\sqrt{x}$

4) $f(x)= \sqrt{x^{5}}*2x^{100}=2x^{2.5}*x^{100}=2x^{102.5}$
$f'(x)=(2x^{102.5})'=2*102.5*x^{101.5}=205*x^{101}* \sqrt{x}$