What is the derivative of (1+(10/x)^x) ?

The derivative of (1+(10/x)^x) is (ln(1+(10)/x)-(10}{x+10})(1+\frac{10)/x)^x

What is the first derivative of (1+(10/x)^x) ?

The first derivative of (1+(10/x)^x) is (ln(1+(10)/x)-(10}{x+10})(1+\frac{10)/x)^x

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\frac{d}{d x} ((1 + \frac{10}{x})^{x})

(ln (1 + \frac{10}{x}) - \frac{10}{x + 10}) (1 + \frac{10}{x})^{x}

Solution steps

\frac{d}{d x} ((1 + \frac{10}{x})^{x})

Apply exponent rule:

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

(1 + \frac{10}{x})^{x} = e^{x l n (1 + \frac{10}{x})}

= \frac{d}{d x} (e^{x l n (1 + \frac{10}{x})})

Apply the chain rule:

e^{x l n (1 + \frac{10}{x})} \frac{d}{d x} (x ln (1 + \frac{10}{x}))

= e^{x l n (1 + \frac{10}{x})} \frac{d}{d x} (x ln (1 + \frac{10}{x}))

\frac{d}{d x} (x ln (1 + \frac{10}{x})) = ln (1 + \frac{10}{x}) - \frac{10}{x + 10}

= e^{x l n (1 + \frac{10}{x})} (ln (1 + \frac{10}{x}) - \frac{10}{x + 10})

e^{x l n (1 + \frac{10}{x})} = (1 + \frac{10}{x})^{x}

= (ln (1 + \frac{10}{x}) - \frac{10}{x + 10}) (1 + \frac{10}{x})^{x}

cos (t) + t sin (t)

\int 6 x - 7 d x

\frac{d}{d x} (I n^{3} x)

\int \frac{ln ( 9 x ^{2} - 1 )}{x ^{3}} d x

3 x^{2} + 5

What is the derivative of (1+(10/x)^x) ?
The derivative of (1+(10/x)^x) is (ln(1+(10)/x)-(10}{x+10})(1+\frac{10)/x)^x
What is the first derivative of (1+(10/x)^x) ?
The first derivative of (1+(10/x)^x) is (ln(1+(10)/x)-(10}{x+10})(1+\frac{10)/x)^x