M mikeb New member Joined Jul 2, 2005 Messages 6 Jul 7, 2005 #1 Find f ' (x): f(x)= (x + csc(x^3 +3)) ^-3 i got as far as : f ' (x)= -3(x + csc(x^3 +3))^-4 * (1 -csc cotx(x^3 +3)) * (3x^2) but im not sure where to go from here, do i just simplify and combine like terms?
Find f ' (x): f(x)= (x + csc(x^3 +3)) ^-3 i got as far as : f ' (x)= -3(x + csc(x^3 +3))^-4 * (1 -csc cotx(x^3 +3)) * (3x^2) but im not sure where to go from here, do i just simplify and combine like terms?
C ChaoticLlama Junior Member Joined Dec 11, 2004 Messages 199 Jul 7, 2005 #2 f(x) = (x + csc(x^3 +3)) ^-3 You pretty much have the idea, you just need to know that dcsc(x)/dx = -csc(x)cot(x) f'(x) = -3(x + csc(x³ + 3))^-4 * (1 - csc(x³ + 3)cot(x³ + 3) * 3x²) f'(x) = [-3(1 - 3x²csc(x³ + 3)cot(x³ + 3)] / (x + csc(x³ + 3))^4 f'(x) = [9x²csc(x³ + 3)cot(x³ + 3) - 3] / (x + csc(x³ + 3))^4
f(x) = (x + csc(x^3 +3)) ^-3 You pretty much have the idea, you just need to know that dcsc(x)/dx = -csc(x)cot(x) f'(x) = -3(x + csc(x³ + 3))^-4 * (1 - csc(x³ + 3)cot(x³ + 3) * 3x²) f'(x) = [-3(1 - 3x²csc(x³ + 3)cot(x³ + 3)] / (x + csc(x³ + 3))^4 f'(x) = [9x²csc(x³ + 3)cot(x³ + 3) - 3] / (x + csc(x³ + 3))^4
