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3 years ago

Lmk if u cant see it correctly but please someone help me out ‍♀️

Mathematics

1 answer:

Leokris [45]3 years ago

3 0

Soz to bother ya with an incorrect answer, but we cant see it clearly. try screen snipping?

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Find the derivative of ln(cosx²).

RoseWind [281]

Answer:

$\displaystyle \frac{dy}{dx} = -2x \tan (x^2)$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = \ln (\cos x^2)$

Step 2: Differentiate

Logarithmic Differentiation [Derivative Rule - Chain Rule]: $\displaystyle y' = \frac{(\cos x^2)'}{\cos x^2}$
Trigonometric Differentiation [Derivative Rule - Chain Rule]: $\displaystyle y' = \frac{-\sin x^2 (x^2)'}{\cos x^2}$
Basic Power Rule: $\displaystyle y' = \frac{-2x \sin x^2}{\cos x^2}$
Rewrite [Trigonometric Identities]: $\displaystyle y' = -2x \tan (x^2)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

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3 years ago