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Popular >

derivative of ln(e^x+7x+1)

Solution

\frac{d}{d x} (ln (e^{x} + 7 x + 1))

Solution

\frac{e ^{x} + 7}{e ^{x} + 7 x + 1}

Solution steps

\frac{d}{d x} (ln (e^{x} + 7 x + 1))

Apply the chain rule:

\frac{1}{e ^{x} + 7 x + 1} \frac{d}{d x} (e^{x} + 7 x + 1)

= \frac{1}{e ^{x} + 7 x + 1} \frac{d}{d x} (e^{x} + 7 x + 1)

\frac{d}{d x} (e^{x} + 7 x + 1) = e^{x} + 7

= \frac{1}{e ^{x} + 7 x + 1} (e^{x} + 7)

Simplify

\frac{1}{e ^{x} + 7 x + 1} (e^{x} + 7) : \frac{e ^{x} + 7}{e ^{x} + 7 x + 1}

= \frac{e ^{x} + 7}{e ^{x} + 7 x + 1}

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Frequently Asked Questions (FAQ)

What is the derivative of ln(e^x+7x+1) ?
The derivative of ln(e^x+7x+1) is (e^x+7)/(e^x+7x+1)
What is the first derivative of ln(e^x+7x+1) ?
The first derivative of ln(e^x+7x+1) is (e^x+7)/(e^x+7x+1)