Mastering The Product Rule: How To Differentiate The Product Of Two Functions

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.

More Answers:
Mastering The Chain Rule: How To Differentiate The Natural Logarithm Function Lne(X)
Mastering The Power Rule: The Derivative Of X With Respect To X In Calculus
The Derivative Of A Constant: Why D/Dx[C] = 0

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