What Is The Derivative Of F(x) = X²·sin(x)? - Testpoint

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What is the derivative of f(x) = x²·sin(x)?

2x·cos(x)
x²·cos(x)
2x·sin(x) + x²·cos(x)
None of these

Explanation

This is a product of two functions, so we apply the product rule:

$d [u \cdot v]/dx = u^{'} \cdot v + u \cdot v^{'}$

Here,

$u = x^^{2}$ , so $u^{'} = 2 x$
$v = sin(x)$ , so $v' = cos(x)$

Now apply the rule:

$f'(x) = 2x cdot sin(x) + x^2 cdot cos(x)$

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