Howard Anton Calculus 10th Edition Solution Step By Step Official
Find ( \fracdydx ) if ( y = \fracx^2 \sin x\cos x ). Step 1 – Recognize the structure You have a product ( x^2 \cdot \frac\sin x\cos x ), but (\frac\sin x\cos x = \tan x). So rewrite: [ y = x^2 \tan x ] Step 2 – Apply product rule [ \fracdydx = \fracddx(x^2) \cdot \tan x + x^2 \cdot \fracddx(\tan x) ] Step 3 – Differentiate each part [ \fracddx(x^2) = 2x, \quad \fracddx(\tan x) = \sec^2 x ] Thus: [ \fracdydx = 2x \tan x + x^2 \sec^2 x ] Step 4 – Simplify (optional, but Anton often stops here) You could factor (x): [ \fracdydx = x(2\tan x + x \sec^2 x) ]
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Ask: Why did they start there? (e.g., "They factored the numerator before taking the limit.") Write down what you know
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