differentiate (x^2 + 3x + 2) - (4x - 1)
I have a test tomorrow and i'm stuck on this question ):
well to differentiate or find the derivative you would use the "sum or difference rule"
which would be
derivative of first factor minus derivative of second factor
and i think you would have to use the power rule too
i hope you know the power rule if not then
you bring the power out in front of the variable and decrease the power by one (in other words power minus 1)
for example if it is x^3
then you bring 3 out in front and subtract power by one
which gives you 3x^2
now to your question
answer is
(2x + 3) - (4)
it would only be x for 2x because 2-1 = 1 and you don't have to write to the power of one
and derivative of 2 would be zero and same for -1
hope this helps, good luck for your test, i also have one tomorrow :)
To differentiate the given expression (x^2 + 3x + 2) - (4x - 1), we need to apply the rules of differentiation. Let's break it down step by step.
Step 1: Simplify the expression inside the parentheses.
(x^2 + 3x + 2) - (4x - 1) can be rewritten as x^2 + 3x + 2 - 4x + 1.
Step 2: Combine like terms.
The expression becomes x^2 - x + 3.
Step 3: Apply the power rule of differentiation.
The power rule states that if we have a term of the form x^n, where n is a constant, the derivative is given by nx^(n-1).
In our case, we have x^2, and applying the power rule gives us 2x^(2-1) = 2x.
Step 4: Apply the constant rule of differentiation.
The constant rule states that if we have a constant, the derivative is zero.
In our expression, we have -x, and the derivative of a constant multiplied by x is -1.
Step 5: Combine the derivatives of the individual terms.
The derivative of x^2 is 2x, and the derivative of -x is -1.
Therefore, differentiating the expression x^2 - x + 3 gives us 2x - 1.
So, the derivative of (x^2 + 3x + 2) - (4x - 1) is 2x - 1.