Derivative of trigonometric functions
The derivative of sine is cosine and the derivative of cosine is minus sine. Dsin(x) = cos(x) and Dcos(x) = - sin(x)
Find the derivative functions of the functions below
Find the value of the derivative in 𝜋
The function consists of the product of two functions. The product derivation rule is used
We substitute 𝜋
Find the zeros of the derivative function
where n is an integer.
Find the extreme values of the function
Differentiate the function. The sine derivative is cosine and the cosine derivative is minus sine. In addition, in a function, a term with a cosine square is a combined function.
cosine is 0 when
Sine is 1 when
The derivative is always positive before the zeros determined by the angle 𝜋 / 2 and negative thereafter before the zeros determined by 3𝜋 / 2
g '(0) = 2
g '(π) = - 2
So at 𝜋 / 2 + n2𝜋 the function has maximum points and at 3𝜋 / 2 + n2𝜋 the function has minimum points.
The extreme values
In the figure, the graph of the function g(x) in green and the graph of the derivative g'(x) in red.
Derivative of the tangent
Definition of tangent
Then the derivative of the tangent is obtained by the derivation rule of the quotient
The derivative of the tangent is not defined at cosine zeros. Just like the tangent.
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