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

Find the derivative of the following functions.

f:x\longmapsto 3.\sin\left(x\right)+4^x

f'\left(x\right)=-\cos{\left(3x\right)} + 16^x

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

f'\left(x\right)=3\cos{\left(3x\right)} + 16^x

f'\left(x\right)=-3\cos{\left(x\right)} + 4^x

f:x\longmapsto -2\cos\left(x\right)+\log_4{\left(x\right)}\\

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

f'\left(x\right) = 2\sin{\left(x\right)} + \dfrac{1}{4x}

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

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

f:x\longmapsto -4\cdot3^x+\cos{\left(x\right)}

f'\left(x\right) = \left(12^x\right)\ln{\left(3\right)} + \sin{\left(x\right)}

f'\left(x\right) = -4\left(3^x\right) + \sin{\left(x\right)}

f'\left(x\right) = \left(-12^x\right)\ln{\left(3\right)} - \sin{\left(x\right)}

f'\left(x\right) = -4\left(3^x\right)\ln{\left(3\right)} - \sin{\left(x\right)}

f:x\longmapsto -5\log_2{\left(x\right)} + \cos{\left(x\right)}

f'\left(x\right) = \dfrac{-5}{x\ln{2}} -\sin{\left(x\right)}

f'\left(x\right) = \dfrac{-5}{x\ln{2}} +\sin{\left(x\right)}

f'\left(x\right) = \dfrac{-5}{x} -\sin{\left(x\right)}

f'\left(x\right) = -5\cdot x \cdot \ln{2} + \sin{\left(x\right)}

f:x\longmapsto 3e^x + 5^x

f'\left(x\right) = 3e^x + 5^x

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

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

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

f:x\longmapsto 2\cdot6^x + \cos{\left(x\right)}

f'\left(x\right) = 2\cdot 6^x \cdot \ln{6} + \sin{\left(x\right)}

f'\left(x\right) = 2\cdot 6^x \cdot \ln{6} -\sin{\left(x\right)}

f'\left(x\right) = 12^x \cdot \ln{6} -\sin{\left(x\right)}

f'\left(x\right) = 2\cdot 6^x -\sin{\left(x\right)}

f:x\longmapsto -3\ln{\left(x\right)} + 9^x

f'\left(x\right) = \dfrac{-3}{x} + 9^x

f'\left(x\right) = \dfrac{-3}{x} - 81^x

f'\left(x\right) = \dfrac{3}{x} + 9^x \ln{9}

f'\left(x\right) = \dfrac{-3}{x} + 9^x \ln{9}