1. Only true to division. Most likely though when multiplying it's more helpful to have the denominators the same.
2. True
3. False
4. True
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Let's say is "x".
so, "x" is the whole or 10/10 whilst 0.002 is 1/10 then, let's check
Step-by-step explanation:
y = (cos x)^(sin x)
Take log both sides.
ln y = ln ((cos x)^(sin x))
ln y = (sin x) ln (cos x)
Take derivative.
1/y dy/dx = (sin x) (1/cos x) (-sin x) + (cos x) ln (cos x)
dy/dx = y [ (cos x) ln (cos x) − sin x tan x ]
dy/dx = (cos x)^(sin x) [ (cos x) ln (cos x) − sin x tan x ]
Your answer is correct.