What is the derivative of (7+5/x ^x) ?

The derivative of (7+5/x ^x) is (ln(7+5/x)-5/(7x+5))(7+5/x)^x

What is the first derivative of (7+5/x ^x) ?

The first derivative of (7+5/x ^x) is (ln(7+5/x)-5/(7x+5))(7+5/x)^x

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\frac{d}{d x} ((7 + \frac{5}{x})^{x})

(ln (7 + \frac{5}{x}) - \frac{5}{7 x + 5}) (7 + \frac{5}{x})^{x}

Solution steps

\frac{d}{d x} ((7 + \frac{5}{x})^{x})

Apply exponent rule:

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

(7 + \frac{5}{x})^{x} = e^{x l n (7 + \frac{5}{x})}

= \frac{d}{d x} (e^{x l n (7 + \frac{5}{x})})

Apply the chain rule:

e^{x l n (7 + \frac{5}{x})} \frac{d}{d x} (x ln (7 + \frac{5}{x}))

= e^{x l n (7 + \frac{5}{x})} \frac{d}{d x} (x ln (7 + \frac{5}{x}))

\frac{d}{d x} (x ln (7 + \frac{5}{x})) = ln (7 + \frac{5}{x}) - \frac{5}{7 x + 5}

= e^{x l n (7 + \frac{5}{x})} (ln (7 + \frac{5}{x}) - \frac{5}{7 x + 5})

e^{x l n (7 + \frac{5}{x})} = (7 + \frac{5}{x})^{x}

= (ln (7 + \frac{5}{x}) - \frac{5}{7 x + 5}) (7 + \frac{5}{x})^{x}

What is the derivative of (7+5/x ^x) ?
The derivative of (7+5/x ^x) is (ln(7+5/x)-5/(7x+5))(7+5/x)^x
What is the first derivative of (7+5/x ^x) ?
The first derivative of (7+5/x ^x) is (ln(7+5/x)-5/(7x+5))(7+5/x)^x