d/dx(sinx)
To find the derivative of the function f(x) = sin(x) with respect to x, we can use the chain rule and the derivative of the sine function
To find the derivative of the function f(x) = sin(x) with respect to x, we can use the chain rule and the derivative of the sine function.
The chain rule states that if we have a composite function f(g(x)), then the derivative is given by f'(g(x)) * g'(x).
In this case, our composite function is sin(x), which can be written as f(g(x)) = sin(x), with f(u) = sin(u) and g(x) = x.
To find the derivative of sin(x), we start by finding f'(u), the derivative of sin(u) with respect to u. The derivative of sin(u) is cos(u).
Next, we find g'(x), the derivative of x with respect to x. Since x is a variable, its derivative is simply 1.
Now, we can apply the chain rule by multiplying f'(u) and g'(x).
f'(u) * g'(x) = cos(u) * 1 = cos(x)
Therefore, the derivative of f(x) = sin(x) with respect to x, or d/dx(sinx), is cos(x).
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