Derivative rules video BPRP

What is the derivative of (ax^2 + bx + c) with respect to x, where a, b, and c are constants?

• 2ax + b + c

• ax + b

• 2ax + b

• 2ax + c

What is the simplified form of the derivative of sin(x) / (1+cos(x))?

• 1 / (1+cos(x))

• cos(x) / (1+cos(x))

• sin(x) / (1+cos(x))^2

• 1 / (1-cos(x))

Which of the following is an equivalent expression for (1+cos(x)) / sin(x)?

• sec(x) + tan(x)

• csc(x) + cot(x)

• sin(x) + cos(x)

• 1 + cot(x)

What is the derivative of csc(x) + cot(x)?

• csc(x)cot(x) + csc^2(x)

• -csc(x)cot(x) + csc^2(x)

• -csc(x)cot(x) - csc^2(x)

• csc(x)cot(x) - csc^2(x)

What is the derivative of sqrt(3x+1)?

• 1 / (2*sqrt(3x+1))

• 3 / (2*sqrt(3x+1))

• 3x / (2*sqrt(3x+1))

• 1 / (sqrt(3x+1))

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What is the derivative of sin³(x) + sin(x³)?

• 3sin²(x)cos(x) + 3x²cos(x³)

• 3sin²(x) + cos(x³)

• 3cos²(x)sin(x) + cos(x³) * 3x²

• 3sin²(x)cos(x) - 3x²cos(x³)

What is the derivative of 1/x⁴?

• 1/(4x³)

• -4/x⁵

• 4/x⁵

• -4x³

What is the derivative of (1 + cot(x))³?

• 3(1 + cot(x))² csc²(x)

• -3(1 + cot(x))² csc²(x)

• 3(1 + cot(x))²

• -3(1 + cot(x))² sec²(x)

Which differentiation rule is primarily used to find the derivative of x² * (2x³ + 1)¹⁰?

• Product Rule

• Chain Rule

• Quotient Rule

• Power Rule