Question

If y=log5x then dy/dx is​

Answer 1

Answer:

dy/dx=5/log5x

Step-by-step explanation:

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Answer 2

Given,

$\[y = \log 5x\]$

Solution,

Assume that $\[5x = t.\]$

Differentiate the above equation.

$\[\begin{array}{l} \Rightarrow 5x = t\\ \Rightarrow 5dx = dt\\ \Rightarrow 5 = \frac{{dt}}{{dx}}\end{array}\]$

Now, differentiate $\[y = \log t.\]$

$\[\begin{array}{l} \Rightarrow y = \log t\\ \Rightarrow \frac{{dy}}{{dt}} = \frac{1}{t}\end{array}\]$

Therefore,

$\[\begin{array}{l} \Rightarrow \frac{{dy}}{{dx}}\\ \Rightarrow \frac{{dy}}{{dt}} \times \frac{{dt}}{{dx}}\\ \Rightarrow \frac{1}{t} \times 5\end{array}\]$

Apply values.

$\[\begin{array}{l} \Rightarrow \frac{5}{{5x}}\\ \Rightarrow \frac{1}{x}\end{array}\]$

Hence, the value is $\[\frac{1}{x}.\]$