Check the solution to "Derivatives Evaluate the following derivatives. ddx(xln⁡x3)"

gorovogpg

Answered question

2022-01-15

Derivatives Evaluate the following derivatives.

\frac{d}{d x} (x {\ln x}^{3})

Jonathan Burroughs

Beginner2022-01-16Added 37 answers

Given,

\frac{d}{d x} (x {\ln x}^{3})

On differentiating, we get

\frac{d}{d x} (x {\ln x}^{3}) = \frac{d (x)}{d x} \cdot {\ln x}^{3} + \frac{d ({\ln x}^{3})}{d x} \cdot x [∵ \frac{d (u \cdot v)}{d x} = \frac{d u}{d x} \cdot v + \frac{d v}{d x} \cdot u]

= 1 \cdot {\ln x}^{3} + \frac{1}{x^{3}} \cdot \frac{d (x^{3})}{d x} \cdot x [∵ \frac{d (\ln x)}{d x} = \frac{1}{x}]

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

= \ln (x^{3}) + 3

SlabydouluS62

Skilled2022-01-17Added 52 answers

{(x {\ln x}^{3})}^{'} = x^{'} \cdot {\ln x}^{3} + x \cdot {({\ln x}^{3})}^{'} =

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

= {\ln x}^{3} + 3

Result:

{\ln x}^{3} + 3

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