Question: "Find the derivatives of the following functions with..." - Plainmath

zagonek34

Answered question

2021-12-07

Find the derivatives of the following functions with respect to x and simplify the result

y = \log \frac{3}{x}

Answer & Explanation

SlabydouluS62

Skilled2021-12-08Added 52 answers

Step 1
Given,

y = \log (\frac{3}{x})

Step 2
Now,

∴ y = \log (\frac{3}{x})

Differentiating w.r.t x, we have

\Rightarrow y^{'} = \frac{d}{d x} (\log (\frac{3}{x}))

\Rightarrow y^{'} = \frac{1}{\frac{3}{x}} \frac{d}{d x} (\frac{3}{x})

\Rightarrow y^{'} = \frac{x}{3} (3) \frac{d}{d x} (\frac{1}{x})

\Rightarrow y^{'} = x (- \frac{1}{x^{2}})

\Rightarrow y^{'} = - \frac{1}{x}

∴ y^{'} = - \frac{1}{x}

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