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

Anonymous2012-11-28T14:59:09Z

Favorite 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!