\(\displaystyle{f{{\left({x}\right)}}}={e}^{{{\ln{{x}}}}}-{e}^{{{2}{\ln{{\left({x}^{{{2}}}\right)}}}}}{)}\)
Apply \(\displaystyle{{\ln{{a}}}^{{{n}}}=}{n}{\ln{{a}}}\)
\(f(x)=e^{\ln x)-e^{ln(x^{2})^{2}}}\) Apply \(\displaystyle{\left({x}^{{{m}}}\right)}^{{{n}}}={x}^{{{m}{n}}}\)
\(\displaystyle{f{{\left({x}\right)}}}={e}^{{{\ln{{x}}}}}-{e}^{{{\ln{{x}}}^{{{4}}}}}\)
Recall that \(\ln e^{z}=z\), so
\(\displaystyle{f{{\left({x}\right)}}}={x}-{x}^{{{4}}}\)
Differentiate both sides with respect to x
\(\displaystyle{f}'{\left({x}\right)}={\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left[{x}-{x}^{{{4}}}\right]}\)
Therefore,
\(f'(x)=1-4x^{3}\)
Find the derivatives of the functions.f(x)=e^{\ln x}-e^{2ln(x^{2})})
Expert Answer
Answered 2021-06-05
Author has 12886 answers
Have a similar question?
Relevant Questions
asked 2021-06-04
Find the derivatives of the functions. \(\displaystyle f{{\left({x}\right)}}={\left[ \ln{{\left({e}^{{{x}^{{{2}}}}}\right)}}\right]}- \ln{{\left[{\left({e}^{{{x}^{{{2}}}}}\right)}\right]}}\)
asked 2021-03-09
Find derivatives of the functions defined as follows. \(f(x)=e^{x\sqrt{3x+2}}\)
asked 2021-05-23
Find the derivatives of the functions. \(g(x)=\ln ∣3x−1∣\)
asked 2021-06-23
Find the derivatives F'(t) and F''(t) for each of the following complex-valued functions of the real variable t.
(a)\(\displaystyle{F}{\left({t}\right)}={e}^{{{\left({1}−{i}\right)}{t}}}\)
(b)\(\displaystyle{F}{\left({t}\right)}={e}^{{{3}{i}{t}}}\)
(c) \(\displaystyle{F}{\left({t}\right)}={e}^{{{\left({2}+{3}{i}\right)}{t}}}\)
asked 2021-06-02
Find the derivatives of the functions. \(\displaystyle{h}{\left({x}\right)}={e}^{{{2}{x}^{{{2}}}-{x}+{1}\ {x}{2}{F};{x}}}\)
asked 2021-03-07
Find derivatives of the functions defined as follows. \(y=(te^{t}=2)/(e^{2t}+1)\)
asked 2020-12-28
Find derivatives of the functions defined as follows. \(y=(t^2 e^{(2t)})/(t+e^{(3t)})\)
