Derivative practice

Calculus Level 1

If f ( x ) = x ln ⁡ ( x ) f(x) = x\ln(x) , find the value of f ′ ( e ) f'(e) .


The answer is 2.

Eddie The Head by Eddie The Head , 27, India

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2 solutions

Daniel Liu
Apr 27, 2014

d d x x ln ⁡ x = x ( d d x ln ⁡ x ) + ln ⁡ x ( d d x x ) = x ⋅ 1 x + ln ⁡ x ⋅ 1 = ln ⁡ x + 1 ∴ f ′ ( e ) = 1 + 1 = 2 \begin{aligned}\dfrac{\text{d}}{\text{d}x}x\ln x &= x\left(\dfrac{\text{d}}{\text{d}x}\ln x\right)+\ln x\left(\dfrac{\text{d}}{\text{d}x}x\right)\\ &= x\cdot \dfrac{1}{x}+\ln x \cdot 1\\ &= \ln x+1\\ &\therefore f'(e)=1+1=\boxed{2}\end{aligned}

5 Helpful 0 Interesting 0 Brilliant 0 Confused

This is wayyyyyyy to easy for most people on Brilliant!! :D

Eddie The Head - 7 years, 1 month ago
Eddie The Head
Apr 27, 2014

I know this is too easy but too tired to come up with a better problem today....

Just differentiate and put x = e x=e .

0 Helpful 0 Interesting 0 Brilliant 0 Confused

You can get ln ⁡ x \ln x to render in LaTeX and not as text in the delimiters (like l n x lnx ) by doing "\ln x" in the delimiters.

Trevor B. - 7 years, 1 month ago

It's a good practice problem for beginning calculus students.

Lukas Leibfried - 5 years, 9 months ago

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