d/dx [f(x) +/- g(x)]=
The expression d/dx [f(x) +/- g(x)] represents the derivative of the sum or difference of two functions, f(x) and g(x), with respect to x
The expression d/dx [f(x) +/- g(x)] represents the derivative of the sum or difference of two functions, f(x) and g(x), with respect to x.
To calculate this derivative, we can use the linearity property of derivatives. The derivative of a sum or difference of functions is equal to the sum or difference of their individual derivatives.
Here is how we can find the derivative:
1. For the sum of two functions: d/dx [f(x) + g(x)]
– Take the derivative of the first function, f(x), with respect to x.
This is represented as df(x)/dx or f'(x).
– Take the derivative of the second function, g(x), with respect to x.
This is represented as dg(x)/dx or g'(x).
– Add the two individual derivatives together: f'(x) + g'(x).
– The final result is the derivative of the sum: d/dx [f(x) + g(x)] = f'(x) + g'(x).
2. For the difference of two functions: d/dx [f(x) – g(x)]
– Take the derivative of the first function, f(x), with respect to x: df(x)/dx or f'(x).
– Take the derivative of the second function, g(x), with respect to x: dg(x)/dx or g'(x).
– Subtract the second derivative from the first one: f'(x) – g'(x).
– The final result is the derivative of the difference: d/dx [f(x) – g(x)] = f'(x) – g'(x).
In summary, the derivative of the sum of two functions is equal to the sum of their individual derivatives, whereas the derivative of the difference of two functions is equal to the difference of their individual derivatives.
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