Question

If f(x)=x4+2cos(x) / 2sin(x), find f′(π/2).

Answer 1

whats our derivative?

Answer 2

f(x) = 4x^3 + (-2sinx) (2sinx) + (x^4 +cosx) ( 2cosx) / 2sinx^2

Answer 3

f(x)=x^4+2cos(x) / 2sin(x)

f(x)=x^4 csc(x) + cot(x)

f(x)= 4x^3 csc(x) -x^4 cot(x)csc(x) - csc^2(x)

Answer 4

i forgot the /2 on the first term doh

Answer 5

\[f \left( x \right)=\frac{ x^4 +2\cos \left( x \right) }{ 2\sin \left( x \right) }\,\, \text{ or } f \left( x \right)= x^4 +\frac{2\cos \left( x \right) }{ 2\sin \left( x \right) }\]

Answer 6

f(x)= 2x^3 csc(x) -x^4 cot(x)csc(x)/2 - csc^2(x)

Answer 7

csc(pi/2) = sin(pi/2) = 1 sooo

Answer 8

isnt cot(pi/2) = 0 since its perp to a vertical slope?

Answer 9

i don't know much about trig

Answer 10

then youll need more practice. trig id 98% memorization

Answer 11

** trig is ....

Answer 12

why did you use csc?

Answer 13

tangent is the slope of a line thru the center of a circle .... pi/2 is 90 degrees is attributed to 1/0 cotangent is the reciprocal of tangent giving us 0/1

Answer 14

1/sin=csc

Answer 15

instead of the quotient rule, i just broke it all apart and used trig identities

Answer 16

okay thx i think i got it now!

Answer 17

yw, my work of it my have some errors so i hope you dont use it verbatim