How do you find the derivative of #f(x)=x+1#?

Answer 1

#dy/dx (x+1) = 1#

Using the power rule, the power of the #x# gets multiplied by the coefficient of #x# and subtracted by 1. So for a term like #6x^2# the differential is #2*6x^(2-1) = 12x^1 = 12x#.

For #x# the differential is simple #1*x^(1-1) = 1*x^0 = 1#

The differential of any constant is always 0. So #dy/dx x+1 = 1 + 0 = 1#

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Answer 2

Paisley Johnson

To find the derivative of ( f(x) = x + 1 ), you can use the power rule for differentiation. The power rule states that if ( f(x) = x^n ), then ( f'(x) = nx^{n-1} ).

For ( f(x) = x + 1 ), the derivative is ( f'(x) = 1 ) because the derivative of ( x ) with respect to ( x ) is ( 1 ) (applying the power rule) and the derivative of a constant (in this case, ( 1 )) is ( 0 ). So, the derivative of ( f(x) = x + 1 ) is simply ( f'(x) = 1 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.