Derivative of sin x
The derivative of sin x is calculated using the chain rule and the derivative of the function cosine
The derivative of sin x is calculated using the chain rule and the derivative of the function cosine.
The derivative of sin x can be denoted as d/dx(sin x) or simply as sin'(x).
Using the chain rule, we have:
d/dx(sin x) = d/dx(cos(π/2 – x))
Let’s denote g(x) = cos(π/2 – x), then the derivative of g(x) with respect to x is:
g'(x) = -sin(π/2 – x)
Finally, using the chain rule, the derivative of sin x can be expressed as:
d/dx(sin x) = -sin(π/2 – x)
This means that the derivative of sin x is equal to the negative of the sine of the complement of x with respect to π/2.
In simpler terms, the derivative of sin x gives us the rate of change of the sine function at any point x. It tells us how fast the sine function is increasing or decreasing at a particular value of x.
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