Derivatives by Rule

Differentiate y= 12x^-2

• 24x^-1
• -24x^-3
• -24x^-1
• 6x^-3

Find the second derivative of the function:
f (x) =  2x - 5x⁶

• f ''(x)= 2 - 30x
• f ''(x) =  2-30x⁵
• f ''(x) = -30x⁵
• f ''(x) = -150x⁴

FInd the derivative:
 $f\left(x\right)=\frac{-2}{3}x^3-\frac{1}{2}x^2+9x$  

• -2x² - x + 9

• -2x² + x + 9

• 2x² - x + 9

• 2x² - x - 9

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

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

Differentiate
 $f\left(x\right)=\frac{2}{x^5}-5$  

• x⁵-3

• -10x⁶

• x⁵-5

• -10x^-6

Find  $\frac{\text{d}y}{\text{d}x}$  for  $y=\frac{2x^4-x^2+3}{2x}$   

•  $3x^2-2$  

•  $3x^2$  

•  $4x^3-x$  

•  $3x^2-\frac{1}{2}-\frac{3}{2x^2}$  

Find y' for  $y=\sqrt{x^3}$  

•  $\frac{3}{2}\sqrt{x}$  

•  $\frac{1}{3\sqrt{x}}$  

•  $3x^2$  

•  $\sqrt{3x^2}$  

What is the derivative of cosx

• $\frac{1}{\sin x}$

• cosx

• sinx

• -sinx

 $f\left(x\right)=\sin x$  Find the slope of the tangent line to f(x) at  $x=\frac{\pi}{6}$  

•  $\frac{1}{2}$  

•  $\frac{\sqrt{3}}{2}$  

•  $\frac{-\sqrt{3}}{2}$  

•  $\frac{-1}{2}$  

 $y=\tan x$  Find y'

•  $\sec^2x$  

•  $\sec x$  

•  $\cos x\sin x$  

•  $-\csc x$