Derivatives

Derivative means the same thing as

• slope of the tangent line

• slope of the normal line

• slope of the secant line

• the function’s value

Find the slope of the Normal line to: $f\left(x\right)\ =\ \frac{4\sqrt{x}}{5}$  
at x = 16

•  $\frac{2}{5}$  

•  $-\frac{1}{160}$  

•  $\frac{1}{10}$  

•  $-10$  

What is the derivative of xⁿ?

• (n-1)xⁿ
• nxⁿ⁺¹
• (n+1)x^n-1
• nx^n-1

Differentiate y= x³ + 2x

• 3x³+2x
• 3x²+2
• 3x+2
• 3x

Find the derivative of the given equation
f(x) = x⁴ + 4x³ - 2x²

• x³ + x² - x
• 4x³ + 12x² + 4x
• 4x + 12x - 4x
• 4x³ + 12x² - 4x

FInd the derivative:
f(x) = (-2/3)x³ - (1/2)x² + 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

Find the derivative.

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx

Find the derivative f(x) = xe^x

• f'(x) = e^x

• f'(x) = xe^x + xe^x

• f'(x) = e^x - xe^x

• f'(x) = e^x + xe^x

.

• (3x²-2)cos(x³-2x)

• -(3x²-2)cos(x³-2x)

• cos(2x²-2)

• sin(2x²-2)