CALC HON MIDTERM 2023

• 4x²+8x+1
• 20x⁶+5x⁴
• 28x⁶+5x⁴-16x

Calculate the derivative, if f(x) = -25xcos(x)

• f'(x)= -25xsin(x) + 25cos(x)

• f'(x)= -25xsin(x) - 25cos(x)

• f'(x)= 25xsin(x) - 25cos(x)

Given that y = (x+2)/(x-3), find y'.

• y' = -1/(x-3)²
• y' = -5/(x-3)²
• y' = (2x-5)/(x-3)²
• y' = (2x-1)/(x-3)²

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

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Find an equation of the tangent line to the graph of f(x) at the point (1, 100)
f(x) = (5x⁵ + 5)²

• y = 500x + 400
• y = 100x + 400
• y = -500 x - 400
• y = 500x - 400

Which of the following is the derivative of g(x)= (x²)(2x⁴ + 2)⁵ ?

• g^'(x)= (2x)(2x⁴ + 2) ⁵ + (x²)(5(2x⁴ + 2)⁴(8x³))

• g^'(x)= 2x + 8x³

• g^'(x)= (2x)(2x⁴ + 2)⁵ + (x²)(8x³)

• g^'(x)= (2x)(5(2x⁴ + 2)⁵(8x³)) + (x²)(2x⁴ + 2)

• 19.79898987

• 16.97056275

• 13.85640646

• 28.28427125