## MITL3ARN3R 4 years ago can someone please explain to me how the derivative of f(x)=sin x is?? and how its found.

1. amistre64

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

2. MITL3ARN3R

so, theres no cosine involved in the answer.

3. amistre64

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)

4. amistre64

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

5. amistre64

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

6. amistre64

0 + cos(x) = cos(x) Dx(sin(x)) = cos(x)

7. Annand

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

8. MITL3ARN3R

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

9. MITL3ARN3R

go for it bro dont be shamed

10. amistre64

x+h-x .... = h

11. Annand

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

12. MITL3ARN3R

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

13. Annand

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

14. Annand

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

15. MITL3ARN3R

yeah

16. Annand

got it?

17. MITL3ARN3R

no , LOL, ill get it though thats a promise