Post

Created by @nathanedwards
 at November 1st 2023, 6:56:36 am.

AP Calculus AB Exam Question:

Find the derivative of the function

f(x)=3x22x+4f(x) = 3x^2 - 2x + 4

Step-by-Step Solution:

To find the derivative of the given function, we can use the power rule of differentiation. According to the power rule, if we have a function of the form f(x)=axnf(x) = ax^n, where aa and nn are constants, then the derivative of f(x)f(x) with respect to xx is f(x)=anxn1f'(x) = anx^{n-1}.

So, applying the power rule, let's find the derivative of f(x)f(x):

f(x)=ddx(3x22x+4)f'(x) = \frac{d}{dx} (3x^2 - 2x + 4)

Using the power rule, we differentiate each term separately:

f(x)=ddx(3x2)ddx(2x)+ddx(4)f'(x) = \frac{d}{dx} (3x^2) - \frac{d}{dx} (2x) + \frac{d}{dx} (4)
f(x)=3ddx(x2)2ddx(x)+ddx(4)f'(x) = 3 \cdot \frac{d}{dx} (x^2) - 2 \cdot \frac{d}{dx} (x) + \frac{d}{dx} (4)

Applying the power rule to each term:

f(x)=32x2121x11+0f'(x) = 3 \cdot 2x^{2-1} - 2 \cdot 1x^{1-1} + 0
f(x)=6x2f'(x) = 6x - 2

Therefore, the derivative of the function f(x)=3x22x+4f(x) = 3x^2 - 2x + 4 is f(x)=6x2f'(x) = 6x - 2.