Generating...                               s20quiz08_n13

  1. Find the equation of the tangent line to $y = -x+3\,\sqrt{x}-2 $ at $x = 4 $ .

    $\displaystyle y=9-{{9\,x}\over{4}}$ $\displaystyle y=1-{{x}\over{4}}$ $\displaystyle y=9-{{x}\over{4}}$ $\displaystyle y=1-{{9\,x}\over{4}}$

  2. Find the derivative $f'(x)$ for $f(x) = -2\,x^2-x^{{{4}\over{3}}}-1 $ .

    $f'(x) =\displaystyle -2\,x^2-x^{{{4}\over{3}}} $ $f'(x) =\displaystyle -4\,x-{{4\,x^{{{1}\over{3}}}}\over{3}}-1 $ $f'(x) =\displaystyle -2\,x-x^{{{1}\over{3}}} $ $f'(x) =\displaystyle -4\,x-{{4\,x^{{{1}\over{3}}}}\over{3}} $

  3. Find the derivative $f'(x)$ for $f(x) = \displaystyle {{2-x}\over{x-3}} $ .

    $f'(x) = \displaystyle -{{1}\over{x^2-6\,x+9}} $ $f'(x) = \displaystyle {{2\,x}\over{x^2-6\,x+9}} $ $f'(x) = \displaystyle -{{2\,x}\over{x^2-6\,x+9}} $ $f'(x) = \displaystyle {{1}\over{x^2-6\,x+9}} $

  4. Find the derivative $f'(x)$ for $f(x) = \displaystyle x^4 + \frac{1} { \sqrt[ 3 ]{x^{ 6 } } }$ .

    $f'(x) =\displaystyle 4\,x^3-{{1}\over{x^2}} $ $f'(x) =\displaystyle 4\,x^3-{{2}\over{x^3}} $ $f'(x) =\displaystyle 4\,x^3+2\,x $ $f'(x) =\displaystyle 4\,x^3+1 $

  5. Suppose that $g'( 8 ) = -2 $. Then find the derivative $f'( 8 )$ for $f(x) = -3\,g\left(x\right)-2\,x^{{{2}\over{3}}} $ .

    $\displaystyle -{{8}\over{3}}$ −8 $\displaystyle -{{2}\over{3}}$ $\displaystyle {{16}\over{3}}$

  6. Suppose that $g( 3 ) = -3 $ and $g'( 3 ) = -1 $. Then find the equation of the tangent line to $y = \displaystyle {{g\left(x\right)}\over{x-4}} $ at $x = 3 $ .

    y = 4x + 9 y = 4x − 9 y = −2x − 9 y = 9 − 2x

  7. Suppose that $g( 4 ) = -1 $ and $g'( 4 ) = -1 $. Then find the derivative $f'( 4 )$ for $f(x) = \displaystyle x^{{{3}\over{2}}}\,g\left(x\right) $ .

    −8 0 $\displaystyle -x^{{{3}\over{2}}}$ $\displaystyle -x^{{{3}\over{2}}}-{{3\,\sqrt{x}}\over{2}}$ −11 −1

  8. Find the derivative $f'(x)$ for $f(x) = \displaystyle\frac{ 3\,x^2-2\,x+4 } { \sqrt{x} }$ .

    $f'(x) =\displaystyle {{9\,x^{{{3}\over{2}}}}\over{2}}-\sqrt{x}-{{2}\over{\sqrt{x}}} $ $f'(x) =\displaystyle 12\,x^{{{3}\over{2}}}-4\,\sqrt{x} $ $f'(x) =\displaystyle {{9\,\sqrt{x}}\over{2}}-{{1}\over{\sqrt{x}}}-{{2}\over{x^{{{3 }\over{2}}}}} $ $f'(x) =\displaystyle 6\,\sqrt{x}+{{2}\over{\sqrt{x}}} $ $f'(x) =\displaystyle 6\,\sqrt{x}-{{2}\over{\sqrt{x}}} $ $f'(x) =\displaystyle 6-{{2}\over{x}} $

  9. Find the derivative $f'(x)$ for $f(x) =\displaystyle 3\,x^2\,e^{x} $ .

    $f'(x) =\displaystyle x^2\,e^{x}+2\,x\,e^{x} $ $f'(x) =\displaystyle 6\,x\,e^{x} $ $f'(x) =\displaystyle 3\,x^2\,e^{x}+6\,x\,e^{x} $ $f'(x) =\displaystyle e^{x}+6\,x $

  10. Find the derivative $f'(x)$ for $f(x) = \displaystyle {{3\,x-e^{x}}\over{e^{x}+1}} $.

    $f'(x) = \displaystyle -{{\left(3\,x-2\right)\,e^{x}-3}\over{e^{2\,x}+2\,e^{x}+1}} $ $f'(x) = \displaystyle -{{\left(3\,x-4\right)\,e^{x}-3}\over{e^{2\,x}+2\,e^{x}+1}} $ $f'(x) = \displaystyle {{\left(3\,x-4\right)\,e^{x}-3}\over{e^{2\,x}+2\,e^{x}+1}} $ $f'(x) = \displaystyle {{\left(3\,x-2\right)\,e^{x}-3}\over{e^{2\,x}+2\,e^{x}+1}} $


Department of Mathematics
Last modified: 2026-03-24