What is the derivative of ln(e^x-e^a) ?

The derivative of ln(e^x-e^a) is (e^x)/(e^x-e^a)

What is the first derivative of ln(e^x-e^a) ?

The first derivative of ln(e^x-e^a) is (e^x)/(e^x-e^a)

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Popular >

\frac{d}{d x} (ln (e^{x} - e^{a}))

\frac{e ^{x}}{e ^{x} - e ^{a}}

Solution steps

\frac{d}{d x} (ln (e^{x} - e^{a}))

Apply the chain rule:

\frac{1}{e ^{x} - e ^{a}} \frac{d}{d x} (e^{x} - e^{a})

= \frac{1}{e ^{x} - e ^{a}} \frac{d}{d x} (e^{x} - e^{a})

\frac{d}{d x} (e^{x} - e^{a}) = e^{x}

= \frac{1}{e ^{x} - e ^{a}} e^{x}

Simplify

\frac{1}{e ^{x} - e ^{a}} e^{x} : \frac{e ^{x}}{e ^{x} - e ^{a}}

= \frac{e ^{x}}{e ^{x} - e ^{a}}

\frac{d}{d x} (e^{x^{2} + 9 x})

\int sec^{3} (x) tan^{5} (x) d x

\int 2 x^{3} d x

\int - \frac{1}{2} \cdot sin (2 x) + \frac{1}{4} \cdot 2 x d x

\int x^{5} + 1 d x

What is the derivative of ln(e^x-e^a) ?
The derivative of ln(e^x-e^a) is (e^x)/(e^x-e^a)
What is the first derivative of ln(e^x-e^a) ?
The first derivative of ln(e^x-e^a) is (e^x)/(e^x-e^a)