Derivative by first principle logsecx²
1 answer:
Answer:
![\displaystyle \frac{d}{dx}[\log \big( \sec (x^2) \big)] = \frac{2x \tan x^2}{\ln 10}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Clog%20%5Cbig%28%20%5Csec%20%28x%5E2%29%20%5Cbig%29%5D%20%3D%20%5Cfrac%7B2x%20%5Ctan%20x%5E2%7D%7B%5Cln%2010%7D)
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]: ![\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>

<u>Step 2: Differentiate</u>
- Logarithmic Differentiation [Derivative Rule - Chain Rule]:

- Trigonometric Differentiation [Derivative Rule - Chain Rule]:

- Simplify:

- Basic Power Rule:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
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Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
10 dm = 1 m
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