Generating...                               quiz12_n23

  1. Find the derivative $f'(x)$ for $f(x) =\displaystyle {{1}\over{\sqrt{\sqrt{x^2+1}+1}}} $ .

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

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

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

  3. Find the derivative $f'(x)$ for $f(x) =\displaystyle \sqrt{x+{{1}\over{\sqrt{x}}}} $ .

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

  4. Find the derivative $f'(x)$ for $f(x) = \displaystyle \sqrt[ 4 ]{ \left(x^2+3\,x+3\right)^5 }$ .

    $f'(x) =\displaystyle {{5\,\left(2\,x+3\right)\,\left(x^2+3\,x+3\right)^{{{1}\over{4}}} }\over{4}} $ $f'(x) =\displaystyle {{5\,x^{{{1}\over{4}}}\,\left(x^2+3\,x+3\right)^{{{5}\over... ...4}}}\,\left(2\,x+3\right)\,\left(x^2+3 \,x+3\right)^{{{1}\over{4}}}}\over{4}} $ $f'(x) =\displaystyle {{5\,\left(x^2+3\,x+3\right)^{{{1}\over{4}}}}\over{4}} $ $f'(x) =\displaystyle \left(2\,x+3\right)\,\left(x^2+3\,x+3\right)^{{{5}\over{4}}} $ $f'(x) =\displaystyle \left(x^2+3\,x+3\right)^{{{9}\over{4}}} $

  5. Find the derivative $f'(x)$ for $f(x) =\displaystyle {{1}\over{2^{\tan x}}} $ .

    $f'(x) =\displaystyle -{{\ln 2\,\tan x}\over{2^{\tan x}}} $ $f'(x) =\displaystyle {{\left(\sec x\right)^2\,\tan x}\over{2^{\tan x}}} $ $f'(x) =\displaystyle -{{\ln 2}\over{2^{\tan x}}} $ $f'(x) =\displaystyle -{{\ln 2\,\left(\sec x\right)^2}\over{2^{\tan x}}} $ $f'(x) =\displaystyle {{\tan ^2x}\over{2^{\tan x}}} $

  6. Find the derivative $f'(x)$ for $f(x) =\displaystyle \tan ^4x $ .

    $f'(x) =\displaystyle 4\,\left(\cot x\right)^3\,\left(\csc x\right)^2 $ $f'(x) =\displaystyle 4\,\left(\sec x\right)^2\,\tan ^3x $ $f'(x) =\displaystyle -4\,\left(\cot x\right)^3\,\left(\csc x\right)^2 $ $f'(x) =\displaystyle -4\,\left(\sec x\right)^2\,\tan ^3x $

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

    $f'(x) =\displaystyle \sqrt{x}\,\left(x^3\,e^{x}+3\,x^2\,e^{x}\right) $ $f'(x) =\displaystyle {{x^{{{5}\over{2}}}\,e^{\sqrt{x}}}\over{2}}+3\,x^2\,e^{\sqrt{x}} $ $f'(x) =\displaystyle x^3\,e^{x}+3\,x^2\,e^{x} $ $f'(x) =\displaystyle {{x^{{{5}\over{2}}}\,e^{\sqrt{x}}}\over{2}} $ $f'(x) =\displaystyle {{3\,x^{{{3}\over{2}}}\,e^{\sqrt{x}}}\over{2}} $

  8. Find the derivative $f'(x)$ for $f(x) =\displaystyle {{1}\over{3^{x}}} $ .

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

  9. Find the derivative $f'(x)$ for $f(x) =\displaystyle e^x \cos \sqrt{x} $ .

    $f'(x) =\displaystyle -{{\cos \sqrt{x}\,e^{x}}\over{2\,\sqrt{x}}}-\sin \sqrt{x}\,e^{x} $ $f'(x) =\displaystyle {{\cos \sqrt{x}\,e^{x}}\over{2\,\sqrt{x}}}+\sin \sqrt{x}\,e^{x} $ $f'(x) =\displaystyle {{\sin \sqrt{x}\,e^{x}}\over{2\,\sqrt{x}}}-\cos \sqrt{x}\,e^{x} $ $f'(x) =\displaystyle \cos \sqrt{x}\,e^{x}-{{\sin \sqrt{x}\,e^{x}}\over{2\,\sqrt{x}}} $

  10. Find the derivative $f'(x)$ for $f(x) =\displaystyle \cos \cos x $ .

    $f'(x) =\displaystyle \cos x\,\sin x\,\sin \cos x-\sin x\,\cos \cos x $ $f'(x) =\displaystyle -\sin x\,\cos \cos x $ $f'(x) =\displaystyle -\sin \cos x $ $f'(x) =\displaystyle \sin x\,\sin \cos x $ $f'(x) =\displaystyle \cos x\,\cos \cos x $


Department of Mathematics
Last modified: 2025-12-16