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

The derivative of (x+ln(x)^5) is 5(x+ln(x))^4(1+1/x)

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

The first derivative of (x+ln(x)^5) is 5(x+ln(x))^4(1+1/x)

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

5 (x + ln (x))^{4} (1 + \frac{1}{x})

Solution steps

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

Apply the chain rule:

5 (x + ln (x))^{4} \frac{d}{d x} (x + ln (x))

= 5 (x + ln (x))^{4} \frac{d}{d x} (x + ln (x))

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

= 5 (x + ln (x))^{4} (1 + \frac{1}{x})

What is the derivative of (x+ln(x)^5) ?
The derivative of (x+ln(x)^5) is 5(x+ln(x))^4(1+1/x)
What is the first derivative of (x+ln(x)^5) ?
The first derivative of (x+ln(x)^5) is 5(x+ln(x))^4(1+1/x)