Best solutions to - "Find the derivative of the following functions y=(x2+1)ln⁡x" - Plainmath

tricotasu

Answered question

2021-10-08

Find the derivative of the following functions

y = (x^{2} + 1) \ln x

Answer & Explanation

Maciej Morrow

Skilled2021-10-09Added 98 answers

Step 1
Given:

y = (x^{2} + 1) \ln x

we know that

\frac{d}{d x} (u \cdot v) = v \frac{d u}{d x} + u \frac{d v}{d x}

...(1)
Step 2
so, by using equation(1)

\frac{d y}{d x} = \frac{d}{d x} [(x^{2} + 1) \ln x]

= (\ln x) \frac{d}{d x} (x^{2} + 1) + (x^{2} + 1) \frac{d}{d x} (\ln x)

(∵ \frac{d}{d x} (x^{n}) = n x^{n - 1}, \frac{d}{d x} (\ln x) = \frac{1}{x})

= (\ln x) (2 x + 0) + (x^{2} + 1) \frac{1}{x}

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

hence, derivative of given function is

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

.

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