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Popular >

derivative of xln(x^9)

Solution

\frac{d}{d x} (x ln (x^{9}))

Solution

9 ln (x) + 9

Solution steps

\frac{d}{d x} (x ln (x^{9}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ln (x^{9})

= \frac{d x}{d x} ln (x^{9}) + \frac{d}{d x} (ln (x^{9})) x

\frac{d x}{d x} = 1

\frac{d}{d x} (ln (x^{9})) = \frac{9}{x}

= 1 \cdot ln (x^{9}) + \frac{9}{x} x

Simplify

1 \cdot ln (x^{9}) + \frac{9}{x} x : 9 ln (x) + 9

= 9 ln (x) + 9

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of xln(x^9) ?
The derivative of xln(x^9) is 9ln(x)+9
What is the first derivative of xln(x^9) ?
The first derivative of xln(x^9) is 9ln(x)+9