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Popular >

derivative of x^9ln|x|

Solution

\frac{d}{d x} (x^{9} ln ∣ x ∣)

Solution

9 x^{8} ln ∣ x ∣ + x^{8}

Solution steps

\frac{d}{d x} (x^{9} ln ∣ x ∣)

Apply the Product Rule:

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

f = x^{9}, g = ln ∣ x ∣

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

\frac{d}{d x} (x^{9}) = 9 x^{8}

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

= 9 x^{8} ln ∣ x ∣ + \frac{1}{x} x^{9}

\frac{1}{x} x^{9} = x^{8}

= 9 x^{8} ln ∣ x ∣ + x^{8}

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\int 2 π y (8 - y^{\frac{3}{2}}) d y

Frequently Asked Questions (FAQ)

What is the derivative of x^9ln|x| ?
The derivative of x^9ln|x| is 9x^8ln|x|+x^8
What is the first derivative of x^9ln|x| ?
The first derivative of x^9ln|x| is 9x^8ln|x|+x^8