Find the derivative of a function of the form x -> f(x).g(x) Calculus

f'\left(x\right)=\dfrac{ \cos{\left(x\right)}}{x} +\sin{\left(x\right)}\log_2{\left(x\right)}

f'\left(x\right)=\dfrac{ \cos{\left(x\right)}}{x\ln{\left(2\right)}} +\sin{\left(x\right)}\log_2{\left(x\right)}

f'\left(x\right)=\dfrac{ \cos{\left(x\right)}}{x\ln{\left(2\right)}} -\sin{\left(x\right)}\log_2{\left(x\right)}

f'\left(x\right)=\dfrac{ \cos{\left(x\right)}}{x} -\sin{\left(x\right)}\log_2{\left(x\right)}

f'\left(x\right)=-\sin^2{\left(x\right)} + \cos^2{\left(x\right)}

f'\left(x\right)=-1

f'\left(x\right)=1

f'\left(x\right)=\sin^2{\left(x\right)} - \cos^2{\left(x\right)}

f'\left(x\right)=2^x\left\{\dfrac{1}{x} + \log_3{\left(x\right)} \right\}

f'\left(x\right)=2^x\left\{\dfrac{1}{x\ln{\left(3\right)}} + \ln{\left(2\right)}\log_3{\left(x\right)} \right\}

f'\left(x\right)=\dfrac{2^x}{x\ln{\left(3\right)}} + \ln{\left(2^x\right)}\log_3{\left(x\right)}

f'\left(x\right)=2^x\left\{\dfrac{1}{x\ln{\left(3\right)}} \cdot \ln{\left(2\right)}\log_3{\left(x\right)} \right\}

f'\left(x\right)=\ln{x}\left(5x^3 + 4x^2 \right)

f'\left(x\right)=\ln{x}\left(4x^3 + 3x^2 +\ln{x}\right) + x^3 + x^2 - \dfrac{1}{x^2}

f'\left(x\right)=\ln{x}\left(4x^3 + 3x^2 + \dfrac{1}{x^2}\right) + x^3 + x^2 - \dfrac{1}{x^2}

f'\left(x\right)=\ln{\left(4x^3 + 3x^2 + \frac{1}{x^2}\right)} + x^3 + x^2 - \dfrac{1}{x^2}

f'\left(x\right) =\dfrac{1}{x}\left( \log_4{\left(x\right)} + \dfrac{\ln{\left(x\right)}}{\ln{4}}\right)

f'\left(x\right) =\dfrac{1}{x}\left( \log_4{4} + 4\dfrac{\ln{\left(x\right)}}{\ln{4}}\right)

f'\left(x\right) =\dfrac{1}{x}\left( \log_4{\left(x\right)} + \ln{\left(x\right)}\right)

f'\left(x\right) =\dfrac{1}{x}\left( \log^2{\left(x\right)} + \ln^2{\left(x\right)}\right)

f'\left(x\right)=2\left(2e\right)^x\ln{2}

f'\left(x\right) = 2\left(2^x \cdot e^x\right)

f'\left(x\right) = 2^x\cdot e^x + 2^x \cdot e^x \cdot \ln{2}

f'\left(x\right) = \left(2e\right)^x + \left(2e\right)^x \ln{2}

f'\left(x\right)= 4^x\left(\cos{x} + \sin{\left(x\right)}\right)

f'\left(x\right)= 4^x\left( \cos{x} -\sin{\left(x\right)}\right)

f'\left(x\right)= 2^x\left(\ln{2}\cdot \cos{x} +\sin{\left(x\right)}\right)

f'\left(x\right)= 2^x\left(\ln{2}\cdot \cos{x} -\sin{\left(x\right)}\right)