Differentiating Trigonometric Functions

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When it comes to differentiating the functions of sin x and cos x, we need to use two fractions of the functions in question, when the variable approaches zero must be considered. They are as follows:

lim sin (x) / x, as x → 0

Limit of sin x / x

lim (cos x - 1) / x as x → 0


Limit cos h - h /h

Based on the above, sin x and cos x can be differentiated as follows:

y = sin x → dy/dx = cos x

Differentiation of sin x
y = cos x → dy/dx = - sin x

Differentiation of cos x


y = tan x  → dy/dx = sec² x

Differentiation of tan x


Differentiation of sine function

Differentiation of sine curve










 

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