What is the derivative of (1+7/x ^x) ?

The derivative of (1+7/x ^x) is (ln(1+7/x)-7/(x+7))(1+7/x)^x

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

The first derivative of (1+7/x ^x) is (ln(1+7/x)-7/(x+7))(1+7/x)^x

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

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

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x ln (1 + \frac{7}{x})) = ln (1 + \frac{7}{x}) - \frac{7}{x + 7}

= e^{x l n (1 + \frac{7}{x})} (ln (1 + \frac{7}{x}) - \frac{7}{x + 7})

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

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

\frac{d}{d x} (x^{3} - 2 x + 3)

\frac{\partial}{\partial x} (ln (x) + 1)

\frac{d}{d x} (ln (x^{- 1}))

\frac{d}{d u} (tan (u))

\int tan^{2} (3 x) d x

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