Quiz for Differentiation

Q1: What is the derivative of sin(x)?

A. cos(x) B. -cos(x) C. sin(x) D. -sin(x)

Q2: What is the derivative of x^n where n is a constant?

A. n*x^(n-1) B. x^n C. n*x^(n+1) D. n*x^n

Q3: The derivative of ln(x) is?

A. 1/x B. ln(x) C. x D. e^x

Q4: What is the derivative of e^x?

A. e^x B. x*e^x C. ln(x) D. 1/x

Q5: What is d/dx(tan(x))?

A. sec^2(x) B. cosec^2(x) C. sec(x) D. cot(x)

Q6: The derivative of a constant is?

A. 0 B. 1 C. The constant itself D. Undefined

Q7: If y = u*v, then dy/dx is?

A. u*dv/dx + v*du/dx B. u/v C. du/dx + dv/dx D. None of these

Q8: If y = u/v, then dy/dx is?

A. (v*du/dx - u*dv/dx)/v^2 B. u*dv/dx + v*du/dx C. (du/dx)/(dv/dx) D. None of these

Q9: What is d/dx(cos(x))?

A. -sin(x) B. cos(x) C. sin(x) D. -cos(x)

Q10: What is the derivative of |x|?

A. x/|x| B. |x| C. x D. 1

Q11: Find the derivative of x^3 + 3x^2 + 5x + 7

A. 3x^2 + 6x + 5 B. x^2 + 2x + 5 C. 6x^2 + 6x + 5 D. 3x^2 + 5x + 6

Q12: d/dx of ln(sin(x)) is?

A. cot(x) B. 1/sin(x) C. cos(x) D. sec(x)

Q13: What is the derivative of arctan(x)?

A. 1/(1+x^2) B. 1/x C. arctan(x) D. x^2

Q14: If y = e^(2x), what is dy/dx?

A. 2e^(2x) B. e^x C. e^(2x) D. 2e^x

Q15: If y = log_10(x), then dy/dx = ?

A. 1/(x ln10) B. 1/x C. log_10(e) D. ln(x)

Q16: d/dx of sec(x) is?

A. sec(x)tan(x) B. tan(x) C. sec(x) D. cosec(x)

Q17: Differentiate x*sin(x)

A. x*cos(x) + sin(x) B. x*sin(x) C. cos(x) D. x + sin(x)

Q18: Find dy/dx if y = ln(x^2 + 1)

A. 2x/(x^2 + 1) B. x/(x + 1) C. 1/(x^2 + 1) D. 2/(x + 1)

Q19: If y = sin^2(x), dy/dx is?

A. 2sin(x)cos(x) B. sin(x) C. 2cos(x) D. cos^2(x)

Q20: What is the second derivative of x^3?

A. 6x B. 3x C. 9x^2 D. x^3