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hard differentiation problems?
DIFFERENTIATE:
1.) f(x) = (cosX + sinX) / (sinXcosX)
2.) y = 37 - sec^3 (2x)
3.)f(x) = (3x^2)/ (x^2 + 2x - 1 )^1/2
1 Answer
- Anonymous8 years agoFavorite Answer
Opposite of that is "easy differentiation questions"! :D Let's get serious here...
1. Rewrite the expression as...
f(x) = 1/sin(x) + 1/cos(x)
= csc(x) + sec(x)
Differentiate the function to get..
f'(x) = -csc(x)cot(x) + sec(x)tan(x)
2. y = 37 - sec³(2x)
Use chain rule to get...
dy/dx = 3sec²(2x) * 2sec(2x) * tan(2x)
3. Use log differentiation to get...
ln(f(x)) = ln(3x²) - ½ln(x² + 2x - 1)
f'(x)/f(x) = 2/x - ½ * (2x + 2)/(x² + 2x - 1)
f'(x) = f(x)(2/x - (x + 1)/(x² + 2x - 1))
f'(x) = 3x²/√(x² + 2x - 1)(2/x - (x + 1)/(x² + 2x - 1))
Good luck!
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