Question

diffrenctiat cos wt with respect to t​

Answer 1

It can be shown from first principles that:

\displaystyle\frac{{{d}{\left( \sin{{x}}\right)}}}{{{\left.{d}{x}\right.}}}= \cos{{x}}

dx

d(sinx)

=cosx

\displaystyle\frac{{{d}{\left( \cos{{x}}\right)}}}{{\left.{d}{x}\right.}}=- \sin{{x}}

dx

d(cosx)

=−sinx

\displaystyle\frac{{{d}{\left( \tan{{x}}\right)}}}{{{\left.{d}{x}\right.}}}={{\sec}^{2}{x}}

dx

d(tanx)

=sec

2

x

Differentiation Interactive Applet - trigonometric functions.

In words, we would say:

The derivative of sin x is cos x,

The derivative of cos x is −sin x (note the negative sign!) and

The derivative of tan x is sec2x.