# How do you find the derivative of #log_10 x#?

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Maybe learn how to base shift

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To find the derivative of ( \log_{10} x ), you can use the logarithmic differentiation method.

Let ( y = \log_{10} x ).

Take the natural logarithm of both sides: ( \ln y = \ln(\log_{10} x) ).

Apply the logarithmic property: ( \ln y = \frac{\ln x}{\ln 10} ).

Differentiate both sides with respect to ( x ): ( \frac{1}{y} \cdot \frac{dy}{dx} = \frac{1}{x \ln 10} ).

Solve for ( \frac{dy}{dx} ): ( \frac{dy}{dx} = \frac{1}{x \ln 10} \cdot y ).

Replace ( y ) with ( \log_{10} x ): ( \frac{dy}{dx} = \frac{1}{x \ln 10} \cdot \log_{10} x ).

So, the derivative of ( \log_{10} x ) is ( \frac{1}{x \ln 10} \cdot \log_{10} x ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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