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Contents
Trigonometric Function
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Trigonometric Functions 
Derivatives
of Sine & Cosine Functions
The
derivatives of the sine and cosine functions can be found from first
principles.
Sine Function:
Let y = f(x) = sin x
The
fourth line uses the factor formulae of trigonometric ratios.
Evaluation
of the limit:
Cosine Function:
Let y = f(x) = cos x
Evaluation
of the limit:
Derivative
of the Tangent Function
The
derivative of tan x can be obtained using the derivatives of sin x
and cos x.
Tangent Function:
In general,
Note
that these rules only stand when the angle is in radians. They are not true
when the angle is in degrees.
Examples
 Differentiate
with respect to x:
(i)
sin 2x
(ii) tan (2x2 + 3)
(iii) cos (ln x)
(iv) esin3x
Solutions:
(i)
d/dx (sin 2x) = 2 cos 2x
(ii)
d/dx [tan (2x2 + 3)] = 4x sec2 (2x2 + 3)
(iii)
(iv)
d/dx (esin3x) = 3 cos 3x . esin3x
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