Expert answers to "Derivatives of Inverse Trigonometric, Logarithmic, and Exponential Functions..."

College
Calculus and Analysis
Differential Calculus
Derivatives

Clifland

Answered question

2021-10-06

Derivatives of Inverse Trigonometric, Logarithmic, and Exponential Functions

y = \ln \sqrt{x^{2} + 5}

Answer & Explanation

timbalemX

Skilled2021-10-07Added 108 answers

Step 1
The function is $y = \ln \sqrt{x^{2} + 5}$
Differentiate the function with respect to x.
$\frac{d y}{d x} = \frac{d}{d x} (\ln \sqrt{x^{2} + 5})$
$= (\frac{1}{\sqrt{x^{2} + 5}}) (\frac{d}{d x} \sqrt{x^{2} + 5})$
$= (\frac{1}{\sqrt{x^{2} + 5}}) (\frac{1}{2 \sqrt{x^{2} + 5}}) (\frac{d}{d x} (x^{2} + 5))$
$= \frac{1}{2 (x^{2} + 5)} (2 x)$
$= \frac{x}{x^{2} + 5}$
Step 2
Thus, the derivative is $\frac{x}{x^{2} + 5}$ .

Jeffrey Jordon

Expert2022-11-14Added 2605 answers

Answer is given below (on video)

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