Question: "Find the derivatives of the functions. f(x)=exlog2|x|"

foass77W

Answered question

2021-06-22

Find the derivatives of the functions.

f (x) = e^{x} \log_{2} | x |

Mayme

Skilled2021-06-23Added 103 answers

f (x) = e^{x} \log_{2} | x |

Diffetrentiate both sides with respect to x

r^{'} (x) = \frac{d}{d x} [e^{x} \log_{2} | x |]

Apply the product rule

r^{'} (x) = e^{x} \frac{d}{d x} [\log_{2} | x |] + \log_{2} | x | \frac{d}{d x} [e^{x}]

Apply

\frac{d}{d x} [{\log_{b} x}^{'} = \frac{1}{x \ln b}

and

\frac{d}{d x} [e^{x}]

r^{'} (x) = e^{x} (\frac{1}{x \ln 2}) + \log_{2} | x | (e^{x})

Factor out

e^{x}

r^{'} (x) = e^{x} (\frac{1}{x \ln 2} + \log_{2} | x |)

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