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Find the derivative of the function. y= x
9+7x−6 x
y ′
=

1 Answer

2 votes

= 9 + 7x - 6x^2 is 7 - 12x

To find the derivative of this function, we need to use the power rule, which states that the derivative of x^n is n*x^(n-1).

Let's start with our function: 9 + 7x - 6x^2. This function is composed of three parts, let's process them separately:

1. The derivative of a constant (like our "9") is always 0. So, the first term of our derivative will be 0.

2. For the second part of our function, "7x", the derivative is the coefficient in front of the "x", since the power of x is 1. Hence, the derivative of "7x" is 7.

3. For the third part, "-6x^2", we apply the power rule. The derivative of x^2 is 2x, so the derivative of "-6x^2" is -6*2*x or -12*x.

Now we can add up all three parts to obtain our derivative:

0 + 7 - 12x

So, the derivative of the function 9 + 7x - 6x^2 is 7 - 12x.

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