Proof for Differentiation

Status
Not open for further replies.
D

Damomeera

Junior Member level 3
Joined
Nov 11, 2012
Messages
30
Helped
0
Reputation
0
Reaction score
0
Trophy points
1,286
Location
Coimbatore
Activity points
1,506
Pls help me with proof
how we say differentiation of sin is cos ?
how we get differentiation of any basic functions ?
 

Damomeera said:
Pls help me with proof
how we say differentiation of sin is cos ?
how we get differentiation of any basic functions ?
Click to expand...

Look onto the sinus function and note its slope as a function of the argument. Surprisingly, you will arrive at the cos function.
 
Damomeera,

d(sin(t)/dt = lim Δt-> 0 of (sin(t+Δt) - sin(t))/Δt = (sin(t)*cos(Δt) + sin(Δt)*cos(t) - sin(t))/Δt

cos(Δt) = 1 as Δt->0 , so the above is (sin(t)+sin(Δt)*cos(t)-sin(t))/Δt = (sin(Δt)*cos(t))/Δt

sin(t)/Δt = 1 as Δt->0, so d(sin(t)/dt = cos(t)

Ratch
 

You can use a graph to prove it. Draw a graph of sin(x) against x. Take tangents at quite a few places. Gradient of tangent is the value of d(sinx)/dx. Draw a curve of d(sinx)/dx against x. You will find that this is a curve for cos(x) against x.

Hope this helps.
Tahmid.
 

Tahmid,

You can use a graph to prove it. Draw a graph of sin(x) against x. Take tangents at quite a few places. Gradient of tangent is the value of d(sinx)/dx. Draw a curve of d(sinx)/dx against x. You will find that this is a curve for cos(x) against x.
Click to expand...

The above is not a proof. It is a verification.

Ratch
 

Status
Not open for further replies.

Similar threads

Menu
Log in
Register
Cookies are required to use this site. You must accept them to continue using the site. Learn more…