Mastering The Sum And Difference Rule Of Derivatives: Simplify Calculus With Easy Techniques

d/dx[u±v]

u’±v’

The derivative of the sum or difference of two functions is equal to the sum or difference of their individual derivatives.

Therefore, we can use the sum and difference rule of derivatives to find the derivative of u ± v with respect to x.

d/dx[u±v] = d/dx[u] ± d/dx[v]

So, if we want to find the derivative of u ± v with respect to x, we simply find the derivative of u with respect to x and add or subtract it from the derivative of v with respect to x, depending on whether we have a plus or minus sign.

For example, if u(x) = 3x^2 and v(x) = 2x^3, then:

d/dx[u + v] = d/dx[3x^2] + d/dx[2x^3]
= 6x + 6x^2 (using the power rule of derivatives)

And,

d/dx[u – v] = d/dx[3x^2] – d/dx[2x^3]
= 6x – 6x^2 (using the power rule of derivatives)

Therefore, the derivative of u ± v with respect to x is simply the sum or difference of the derivatives of u and v, respectively.

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