Proof for Differentiation

[Damomeera]

Pls help me with proof
how we say differentiation of sin is cos ?
how we get differentiation of any basic functions ?

 

[LvW]

Pls help me with proof
how we say differentiation of sin is cos ?
how we get differentiation of any basic functions ?

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

 

[Ratch]

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

 

[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.

Hope this helps.
Tahmid.

 

[Ratch]

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.

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

Ratch