Honors Calc Review for Test 3

Find the derivative of the given equation
f(x) =  $\frac{1}{x^2}$  Hint: rewrite with a negative exponent

• f'(x) = 1/2x

• f'(x) = -2x^-3

• f'(x) = 2x

• f'(x) = -2x

Differentiate y =  $\frac{12}{x^2}$  

• y' = 24x^-1

• y' = -24x^-3

• y' = -24x^-1

• y' = 6x^-3

Differentiate y =  $\frac{12}{x^2}$  

• y' = 24x^-1

• y' = -24x^-3

• y' = -24x^-1

• y' = 6x^-3

Find the derivative of f(x) = 6x³⁰ -2x¹⁵ + 4x³ - 2x + 1

• f'(x) = 18x²⁹ + 30x¹⁵ + 12x³ 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² - 2
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² +1

Find the derivative of $y=4x^3+3x+10$ 

•  $\frac{dy}{dx}=4x^2+3$  

•  $\frac{dy}{dx}=4x^2+3x$  

•  $\frac{dy}{dx}=12x^2+3x$  

•  $\frac{dy}{dx}=12x^2+3$  

Derivative means the same thing as

• slope of the tangent line
• slope of the normal line
• exponent
• slope of the secant line

Find the derivative of:

 $f\left(x\right)=4\sqrt{x}$  

•  $f'\left(x\right)=\frac{2}{\sqrt{x}}$  

•  $f'\left(x\right)=2\sqrt{x}$  

•  $f'\left(x\right)=4x^{\frac{1}{2}}$  

•  $f'\left(x\right)=2x^{-\frac{1}{2}}$  

Find the derivative of:

 $f\left(x\right)=3x^7-6x^6-10x^4+3x^3-15x-21$  

•  $f'\left(x\right)=21x^6-36x^5-40x^3+9x^2-15$  

•  $f'\left(x\right)=3x^6-6x^5-10x^3+3x^2-15$  

•  $f'\left(x\right)=x^6-x^5-x^3+x^2-15$  

•  $f'\left(x\right)=28x^6-30x^5-30x^3+12x^2-15$  

Which of the following means "first derivative"

• f'(x)
• y'
• dy/dx
• all of the above

Find the derivative of  $f\left(x\right)\ =\ \frac{1}{x^5}$  

•  $5x^4$  

•  $-5x^6$  

•  $-\frac{5}{x^6}$  

•  $\frac{1}{5x^6}$