Derivative: Product and Quotient Rules

Find the derivative. f(x) = -8x^-3 + 5x - e^x

• f'(x) = -24x^-4 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x
• f'(x) = 24x^-2 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x-1

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

Find the derivative of f(x) = x²sinx

• f'(x) = 2xsinx - x²cosx
• f'(x) = 2xsinx + x²sinx
• f'(x) = 2xsinx + x²cosx
• f'(x) = 2xcosx

Tags

CCSS.HSA.SSE.B.3

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

•  $-3x^2+12x^3$  

•  $-21x^3+6x$  

•  $-21x^6+6x^2$  

•  $-84x^6-6x^2$  

Tags

CCSS.HSA.APR.A.1

• 8x⁴ -60x²
• 16x⁴
• (8x⁴ -60x²)/(2x²-5)²
• 3x

Tags

CCSS.HSF-IF.C.7D

Derivative means the same thing as

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

Find f'(x) if       
f(x)=(2x-7)/(x+3) 

• 2
• 13/(x+3)²
• -4/(x+3)²
• -13/(x+3)

Tags

CCSS.HSF.IF.A.2

At which point(s) will the slope(s) of the tangent line be POSITIVE?

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

At which point(s) will the slopes of the tangent line be zero?

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Find the derivative of g(x)=(3x-2)/(x²+2)

• 9x²+2
• 3(x²+2)/(x²+2)²
• (-3x²+4x +6)/(x²+2)²
• (-3x²+10)/(x²+2)²