Question

Bài 1: tìm đạo hàm của các hàm số sau

1. y=6x² -\(\dfrac{4}{x}\)+1

2. y=\(\dfrac{2x+1}{-x+1}\)

3. y= \(\sqrt{x^2-3x+4}\)

4. y=\(\dfrac{\left(x^2-1\right)\left(x+3\right)}{x-4}\)

5. y=\(\dfrac{1}{2x^2-3x+5}\)

6. y=(x+1)\(\sqrt{x^2-1}\)

Answer 1

1.

\(y'=12x+\dfrac{4}{x^2}\)

2.

\(y'=\dfrac{3}{\left(-x+1\right)^2}\)

3.

\(y'=\dfrac{2x-3}{2\sqrt{x^2-3x+4}}\)

4.

\(y=\dfrac{x^3+3x^2-x-3}{x-4}\)

\(y'=\dfrac{\left(3x^2+6x-1\right)\left(x-4\right)-\left(x^3+3x^2-x-3\right)}{\left(x-4\right)^2}=\dfrac{2x^3-9x^2-24x+7}{\left(x-4\right)^2}\)

5.

\(y'=-\dfrac{4x-3}{\left(2x^2-3x+5\right)^2}\)

6.

\(y'=\sqrt{x^2-1}+\dfrac{x\left(x+1\right)}{\sqrt{x^2-1}}\)