What is the derivative of xln(x^{10}) ?

The derivative of xln(x^{10}) is 10ln(x)+10

What is the first derivative of xln(x^{10}) ?

The first derivative of xln(x^{10}) is 10ln(x)+10

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\frac{d}{d x} (x ln (x^{10}))

10 ln (x) + 10

Solution steps

\frac{d}{d x} (x ln (x^{10}))

Apply the Product Rule:

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

f = x, g = ln (x^{10})

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

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

\frac{d}{d x} (ln (x^{10})) = \frac{10}{x}

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

Simplify

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

= 10 ln (x) + 10

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

\frac{d}{d x} (- 25 (\frac{x}{x ^{2} + 1}))

\int (8 x + 9) d x

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What is the derivative of xln(x^{10}) ?
The derivative of xln(x^{10}) is 10ln(x)+10
What is the first derivative of xln(x^{10}) ?
The first derivative of xln(x^{10}) is 10ln(x)+10