How to use the chain rule with trigonometric functions
Derivatives of Trigonometric Functions
In the previous article, we discussed the derivative of the trigonometric function expressed by the following formulas,
f(x)

f’(x)

sin x

cos x

cos x

sin x

By using chain theorems,
we can develop derivatives of complex trigonometric functions, such as the
following examples,
Example 1
Find the result of the function derivative y = F(x) = sin 5x.
Answer:
For
example, y = sin u and u = 5x then
Example 2.
Find the result of the
function derivative y = F’(x) = cos (2x – 8)
Answer:
Example 3.
Find the result of the
function derivative y = y = F(x) = sin^{3 }x
Answer:Integral Trigonometry Function
Given that integrals are
antidifferential, we can determine the basic formulas of the following trigonometric
functions,
∫ sin x dx =  cos x + c
∫ cos x dx = sin x + c
find the integral of a
function ∫ 4 sin x dx using the
chain rule.
Answer:
∫ 4 sin x dx =  4 cos x +
c
Example 5.
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