d/dx sin(x)
To find the derivative of sin(x) with respect to x (written as d/dx sin(x)), we can use the chain rule of differentiation
To find the derivative of sin(x) with respect to x (written as d/dx sin(x)), we can use the chain rule of differentiation. The derivative of sin(x) is obtained by multiplying the derivative of the outer function sin(u) with respect to u, and the derivative of the inner function x with respect to x.
The derivative of sin(u) with respect to u is cos(u). In this case, u is x. So, d/dx sin(x) becomes d/dx sin(u), where u = x.
Now, the derivative of x with respect to x is simply 1.
Therefore, applying the product rule, the derivative of sin(x) with respect to x is:
d/dx sin(x) = cos(x) * 1 = cos(x)
So, the derivative of sin(x) with respect to x is cos(x).
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