Question

can someone please explain to me how the derivative of f(x)=sin x is?? and how its found.

Answer 1

lim as h-> 0; sin(x+h)-sin(x)
------------
h

Answer 2

so, theres no cosine involved in the answer.

Answer 3

sin(x+h) = sin(x)cos(h) + sin(h)cos(x)

sin(x)cos(h) + sin(h)cos(x) - sin(x) = sin(x)(cos(h)-1) + sin(h)cos(x)

Answer 4

\[sin(x)\frac{cos(h)-1}{h}+cos(x)\frac{sin(h)}{h}\]

Answer 5

\[\frac{cos(h)-1}{h} \implies 0;\ and \frac{sin(h)}{h} \implies 1\]

Answer 6

0 + cos(x) = cos(x)

Dx(sin(x)) = cos(x)

Answer 7

\[d(\sin x)/dx=\lim_{dx \rightarrow 0} [\sin(x+dx)- \sin(x)]/[x+dx-x]\]
\[d(\sin x)/dx=\lim_{dx \rightarrow 0} [2\cos(x+dx/2)*\sin(dx/2)]/[dx]\]
\[= \lim_{dx \rightarrow 0} [\cos(x+dx/2)]*\ [\sin(dx/2)]/[dx/2]\]
=cos(x)

Answer 8

in the change of delta x, why is h by itself , what were the other two variables that were cancelled out

Answer 9

go for it bro dont be shamed

Answer 10

x+h-x .... = h

Answer 11

\[\lim_{a \rightarrow 0} \sin(a)/a=1\]

Answer 12

i just cant understand it how sin x ends up cos x , the derivative of the function,

Answer 13

sin(A)-sin(B)=2*cos((A+B)/2)*sin((A-B)/2)

Answer 14

hope you know the general eqn for finding derivatives...

Answer 15

yeah

Answer 16

got it?

Answer 17

no , LOL, ill get it though thats a promise