d/dx[uv]=
vu’+uv’
The formula to differentiate the product of two functions is given by the product rule, which states:
d/dx[uv] = u * dv/dx + v * du/dx
Where u and v are functions of x.
Therefore, to differentiate uv with respect to x, we need to first find the derivative of u and v separately. Let’s assume that u and v are differentiable functions.
So, we have:
u = u(x)
v = v(x)
Then,
du/dx = derivative of u with respect to x
dv/dx = derivative of v with respect to x
Now, applying the product rule, we have:
d/dx[uv] = u * dv/dx + v * du/dx
= u(x) * (dv/dx)[v(x)] + v(x) * (du/dx)[u(x)]
Therefore, the derivative of uv with respect to x is given by:
d/dx[uv] = u(x) * (dv/dx)[v(x)] + v(x) * (du/dx)[u(x)]
This is the final answer.
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