Derivatives

Derivatives

Multiple Choice

FInd the derivative:

$$f(x)=-\frac{2}{3}x^3-\frac{1}{2}x^2+9x$$

• -2x² - x + 9

• -2x² + x + 9

• 2x² - x + 9

• 2x² - x - 9

Multiple Choice

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

Multiple Choice

Set up the derivative of y=(3x⁴ - 7)*(5x² + 1)

• (12x³)*(10x)
• (3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)
• (3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)
• (3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

Multiple Choice

Differentiate

$$f(x)=\frac{2}{x^5}-5.$$

• x⁵-3
• -10x⁶ 
• x⁵-5
• -10x^-6 

Multiple Choice

Find the derivative.

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

Multiple Choice

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

Multiple Choice

.

• (3x²-2)cos(x³-2x)

• -(3x²-2)cos(x³-2x)

• cos(2x²-2)

• sin(2x²-2)

Multiple Choice

Find the derivative of

$$g(x)=\frac{3x-2}{x^2+2}$$

• $$9x^2+2$$

• $$\frac{3(x^2+2)}{(x2+2)^2}$$

• $$\frac{-3x^2+4x+6}{(x^2+2)^2}$$

• $$\frac{-3x^2+10}{(x2+2)^2}$$

Multiple Choice

d/dx (sin²x) = ?

• 2sin x
• 2(sin x)(cos x)
• 2cos x
• 2x(cos x)

Multiple Choice

Find the second derivative of:

f(x) = 2x² - 8x + 9

• -8

• 4

• 9

• 0