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Popular >

derivative of x^3ln|1+x|

Solution

\frac{d}{d x} (x^{3} ln ∣ 1 + x ∣)

Solution

3 x^{2} ln ∣ 1 + x ∣ + \frac{x ^{3}}{1 + x}

Solution steps

\frac{d}{d x} (x^{3} ln ∣ 1 + x ∣)

Apply the Product Rule:

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

f = x^{3}, g = ln ∣ 1 + x ∣

= \frac{d}{d x} (x^{3}) ln ∣ 1 + x ∣ + \frac{d}{d x} (ln ∣ 1 + x ∣) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 3 x^{2} ln ∣ 1 + x ∣ + \frac{1}{1 + x} x^{3}

\frac{1}{1 + x} x^{3} = \frac{x ^{3}}{1 + x}

= 3 x^{2} ln ∣ 1 + x ∣ + \frac{x ^{3}}{1 + x}

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

What is the derivative of x^3ln|1+x| ?
The derivative of x^3ln|1+x| is 3x^2ln|1+x|+(x^3)/(1+x)
What is the first derivative of x^3ln|1+x| ?
The first derivative of x^3ln|1+x| is 3x^2ln|1+x|+(x^3)/(1+x)