What Is The Derivative Of X³ Ln(x) With Respect To X? - Testpoint

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What is the derivative of x³ ln(x) with respect to x?

3x² ln(x) + x²
x² + 3x² ln(x)
x³ + ln(x)
None of these

Explanation

We use the product rule since it's the product of two functions:

$f(x) = x^3 cdot ln(x)$

Let:

$u = x^3 Rightarrow u' = 3x^2$
$v = ln(x) Rightarrow v' = frac{1}{x}$

Apply the product rule:

$f^{'} (x) = u^{'} v + u v^{'} = 3 x^^{2} \cdot ln (x) + x^^{3} \cdot 1/x$ $f^{'} (x) = 3^x^{2} ln (x) + x^^{2}$

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