Finding Derivatives using Product Rule

Finding Derivatives using Product Rule

In this lesson we will take notes on a few examples then practice using this derivative rule.

This Rule is 7. The Product Rule

Example 1

Look at how they set this up.

They ask you to differentiate the function that is made up of 2 functions multiplied together.

Let the first multiple be u and the second v, then differentiate them separately. We'll put it back together in the end to make the derivative.

7. f'(x)=u'v + uv'

Multiple Choice

• 5x⁴ + 20x³ - 2
• -160x⁷+140x⁶ - 48x³ - 24x²
• -80x⁷+ 60x⁶ + 32x³ - 24x²

Multiple Choice

• -25x⁷ - 230x⁵ + 10x² - 8
• 125x⁹ - 50x⁴ + 50x³ - 40x
• -175x⁶ + 100x⁴ + 20x
• -50x⁶ + 20x

Multiple Choice

• -36x⁵ + 16x³
• 2x⁴ + 8x³
• -12x⁵
• -6x⁶ - 44x⁴

Multiple Choice

Find the derivative of y = 2x² (3x - 4)

• 6x³ - 8x²
• 18x² - 16x
• 15x² - 6x
• 6x - 4

Multiple Choice

• 3x^2 – x
• x^3 + x^2 + x
• 3x^2

Multiple Choice

Use the product rule to determine the derivative.

• 4x⁸+60x⁶+12x³
• 12x⁷+36x²
• 32x⁷+36x²
• 20x⁶

Multiple Choice

• 4x²+8x+1
• 20x⁶+5x⁴
• 28x⁶+5x⁴-16x

Multiple Choice

Find the derivative of y = 2x² (3x - 4)

• 6x³ - 8x²
• 18x² - 16x
• 15x² - 6x
• 6x - 4

Multiple Choice

Let f(x) = (x - 1)(x + 2). Find f'(0)

• 0

• 1

• 2

• 3

Multiple Choice

Let f(x) = (x - 1)(x + 2). Find f'(0)

• 0

• 1

• 2

• 3

Multiple Choice

Let y = (x - 1)(x + 2). Find dy/dx.

• 2x + 1

• 2x - 1

• 4x - 1

• 2x² + x - 1

Multiple Choice

 $x^2\left(-3x^2-2\right)$  

•  $-6x^3-4x$  

•  $-12x^3-4x$  

•  $12x^3+4x$  

•  $-36x^2-4$  

Multiple Choice

Use the product rule to find the derivative. $f\left(x\right)\ =\ -x^3\left(3x^4-2\right)$  

•  $-3x^2+12x^3$  

•  $-21x^3+6x$  

•  $-21x^6+6x^2$  

•  $-84x^6-6x^2$