Question

найдите производную функции
1) f(x)=3x²$\sqrt{x}$
2)f(x)=x²sinx
3)f(x)=$\frac{ x^{2} -2}{x}$
4)f(x)=(2x-1)³
5)f(x)=$\sqrt{3x+2}$
6)f(x)=ctg$\frac{x}{3}$

Answer 1

1)
$f(x)=3x^2*x^{ \frac{1}{2} }=3x^{2.5} \\ \\ f'(x)=3*2.5x^{1.5}=7.5x \sqrt{x}$

2)
$f'(x)=2xsinx+x^2cosx$

3)
$f'(x)= \frac{2x*x-(x^2-2)}{x^2}= \frac{2x^2-x^2+2}{x^2}= \frac{x^2+2}{x^2}=1+ \frac{2}{x^2}$

4)
$f'(x)=3(2x-1)^2*2=6(2x-1)^2$

5)
$f'(x)= \frac{3}{2 \sqrt{3x+2} }$

6)
$f'(x)=- \frac{1}{3sin^2 \frac{x}{3} }$