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Find dy/dx of the function y = √x sec*-1 (√x)
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Find dy/dx of the function y = √x sec*-1 (√x)
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Mathematics
3 years
2021-07-30T18:30:54+00:00
2021-07-30T18:30:54+00:00 2 Answers
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Answer:
General Formulas and Concepts:
Algebra I
Calculus
Derivatives
Derivative Notation
Basic Power Rule:
Derivative Rule [Product Rule]:![Rendered by QuickLaTeX.com \displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)](https://documen.tv/wp-content/ql-cache/quicklatex.com-e4b4b67d6d3f52209de649728b2d4b23_l3.png)
Derivative Rule [Chain Rule]:![Rendered by QuickLaTeX.com \displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://documen.tv/wp-content/ql-cache/quicklatex.com-9445145c1c36a502b0908f4dd4f6797a_l3.png)
Arctrig Derivative:![Rendered by QuickLaTeX.com \displaystyle \frac{d}{dx}[arcsec(u)] = \frac{u'}{|u|\sqrt{u^2 - 1}}](https://documen.tv/wp-content/ql-cache/quicklatex.com-45f4ecbac80ff6fe61f1a9fc207c15f8_l3.png)
Step-by-step explanation:
Step 1: Define
Identify
Step 2: Differentiate
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Hi there!
Use the chain rule and multiplication rules to solve:
g(x) * f(x) = f'(x)g(x) + g'(x)f(x)
g(f(x)) = g'(f(x)) * ‘f(x))
Thus:
f(x) = √x
g(x) = sec⁻¹ (√x)
Simplify: