Hi guys i have ang assignment due tomorrow....can you please find dy/dx for the following equations?
1. f(x)= (sinx)^√x
2. f(x) = (cosx)^ cosx
1. f(x)= (sinx)^√x
2. f(x) = (cosx)^ cosx
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1.) f(x) = y = (sin x)^(√x)
ln(y) = √x * ln(sin x)
Differentiate both sides:
y'/y = √x*cot(x) + ln(sin x)/(2√x)
y' = [(sin x)^√x ] * [√x*cot x + ln(sin x)/(2√x))]
ln(y) = √x * ln(sin x)
Differentiate both sides:
y'/y = √x*cot(x) + ln(sin x)/(2√x)
y' = [(sin x)^√x ] * [√x*cot x + ln(sin x)/(2√x))]
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Can you natual log each side of the equation. aka
Ln(Y) = sqrt(x)*Ln(sinx) and take the derative of each side.
Ln(Y) = sqrt(x)*Ln(sinx) and take the derative of each side.