First slide

Diffrentiation

Question

If f(x) = x³ $ℓ$ n (x)
Then f '(x) is :

Easy

A

$x^{2} + 3 x^{2} \ln x$
B

$x^{2} (1 + ℓ n x)$
C

$4 x^{2}$
D

None of these

Solution

$\begin{array}{l} \frac{d}{d x} (u v) = u \frac{d v}{d x} + \frac{d u}{d x} v \\ ∴ \frac{d}{d x} (x^{3} \ln x) = (x^{3}) (\frac{1}{x}) + (3 x^{2}) (\ln x) \\ ∴ \frac{d}{d x} (x^{3} \ln x) = x^{2} + 3 x^{2} \ln x \end{array}$

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