What is the derivative of log_{5}(e^x) ?

The derivative of log_{5}(e^x) is log_{5}(e)

What is the first derivative of log_{5}(e^x) ?

The first derivative of log_{5}(e^x) is log_{5}(e)

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\frac{d}{d x} (lo g_{5} (e^{x}))

lo g_{5} (e)

Solution steps

\frac{d}{d x} (lo g_{5} (e^{x}))

Simplify

lo g_{5} (e^{x}) : lo g_{5} (e) x

= \frac{d}{d x} (lo g_{5} (e) x)

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= lo g_{5} (e) \frac{d x}{d x}

Apply the common derivative:

\frac{d x}{d x} = 1

= lo g_{5} (e) \cdot 1

Simplify

= lo g_{5} (e)

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What is the derivative of log_{5}(e^x) ?
The derivative of log_{5}(e^x) is log_{5}(e)
What is the first derivative of log_{5}(e^x) ?
The first derivative of log_{5}(e^x) is log_{5}(e)