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Popular >

derivative of x^{12}ln|x|

Solution

derivative of

x^{12} ln ∣ x ∣

Solution

12 x^{11} ln ∣ x ∣ + x^{11}

Solution steps

\frac{d}{d x} (x^{12} ln ∣ x ∣)

Apply the Product Rule:

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

f = x^{12}, g = ln ∣ x ∣

= \frac{d}{d x} (x^{12}) ln ∣ x ∣ + \frac{d}{d x} (ln ∣ x ∣) x^{12}

\frac{d}{d x} (x^{12}) = 12 x^{11}

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

= 12 x^{11} ln ∣ x ∣ + \frac{1}{x} x^{12}

\frac{1}{x} x^{12} = x^{11}

= 12 x^{11} ln ∣ x ∣ + x^{11}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of x^{12}ln|x| ?
The derivative of x^{12}ln|x| is 12x^{11}ln|x|+x^{11}
What is the first derivative of x^{12}ln|x| ?
The first derivative of x^{12}ln|x| is 12x^{11}ln|x|+x^{11}