d/dx [uv]
To find the derivative of the product of two functions, u(x) and v(x), we use the product rule
To find the derivative of the product of two functions, u(x) and v(x), we use the product rule. The product rule states that if we have two functions f(x) and g(x), the derivative of their product is given by:
(d/dx)[f(x)g(x)] = f(x)(d/dx)[g(x)] + g(x)(d/dx)[f(x)]
We can apply this rule to find the derivative of uv(x):
(d/dx)[uv(x)] = u(x)(d/dx)[v(x)] + v(x)(d/dx)[u(x)]
Therefore, the derivative of uv(x) with respect to x is given by u(x)(d/dx)[v(x)] + v(x)(d/dx)[u(x)].
It’s important to note that the order in which the functions u(x) and v(x) are multiplied matters when using the product rule.
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