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Worksheet: Derivatives of Power and Exponential Functions

Q1:

Find , given that .

  • A
  • B
  • C
  • D

Q2:

Find the first derivative of with respect to .

  • A
  • B
  • C
  • D
  • E

Q3:

Differentiate .

  • A
  • B
  • C
  • D
  • E

Q4:

Differentiate the function .

  • A
  • B
  • C
  • D
  • E

Q5:

Find the first derivative of the function .

  • A
  • B
  • C
  • D

Q6:

Find the third derivative of the function .

  • A
  • B
  • C
  • D

Q7:

Given that the function , and , find the value of .

  • A
  • B
  • C
  • D2

Q8:

Given that , determine .

  • A
  • B
  • C
  • D

Q9:

If , and , find .

  • A
  • B
  • C
  • D

Q10:

Find the first and second derivatives of the function .

  • A,
  • B,
  • C,
  • D,
  • E,

Q11:

List the equations of all the tangents to that also lie on the point .

  • A,
  • B,
  • C,
  • D,

Q12:

Find the point on the curve at which the tangent to the curve is parallel to the -axis.

  • A
  • B
  • C
  • D

Q13:

Find the point that lies on the curve , at which the tangent to the curve is perpendicular to the straight line .

  • A
  • B
  • C
  • D

Q14:

If the line is tangent to the graph of the function at , what is ?

Q15:

Find the positive angle that the tangent to at makes with the positive -axis, giving your answer to the nearest second.

  • A
  • B
  • C
  • D

Q16:

The curves and have a common tangent at . Find , , and .

  • A, ,
  • B, ,
  • C, ,
  • D, ,

Q17:

Find the equation of the tangent to the curve at the point .

  • A
  • B
  • C
  • D