Lesson: The Quotient Rule of Derivatives

In this lesson, we will learn how to find the derivative of quotient functions using the quotient rule of differentiation.

Sample Question Videos

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Worksheet: The Quotient Rule of Derivatives • 25 Questions • 3 Videos

Q1:

Find d d 𝑦 𝑥 if 𝑦 = 𝑥 + 3 𝑥 + 3 2 3 .

Q2:

Find d d 𝑦 𝑥 , given that 𝑦 = 𝑥 + 7 𝑥 + 6 𝑥 + 8 3 2 .

Q3:

Find the first derivative of function 𝑦 = 4 𝑥 9 𝑥 − 7 2 .

Q4:

Differentiate 𝑓 ( 𝑥 ) = 4 𝑥 − 5 𝑥 + 8 3 𝑥 − 4 2 .

Q5:

Suppose 𝑓 ( 𝑥 ) = 𝑥 + 𝑎 𝑥 − 𝑎 and 𝑓 ′ ( 2 ) = − 2 . Determine 𝑎 .

Q6:

Suppose that 𝑓 ( 𝑥 ) = 𝑥 + 𝑎 𝑥 + 𝑏 𝑥 − 7 𝑥 + 4 2 2 . Given that 𝑓 ( 0 ) = 1 and 𝑓 ′ ( 0 ) = 4 , find 𝑎 and 𝑏 .

Q7:

Find the first derivative of 𝑦 = 8 𝑥 + 5 3 𝑥 + 2 2 .

Q8:

Find the first derivative of 𝑦 = 𝑥 − 9 3 𝑥 + 1 3 .

Q9:

Differentiate 𝑓 ( 𝑥 ) = 5 𝑥 − 1 7 𝑥 + 6 2 .

Q10:

Find the first derivative of the function 𝑦 = 4 𝑥 + 5 𝑥 + 5 4 𝑥 − 2 𝑥 + 3 2 2 .

Q11:

Given that 𝑦 = 3 √ 𝑥 − 2 𝑥 √ 𝑥 , determine d d 𝑦 𝑥 .

Q12:

Find the first derivative of 𝑦 = − 3 𝑥 − 2 𝑥 + 1 7 √ 𝑥 2 with respect to 𝑥 .

Q13:

If 𝑦 = 2 9 𝑥 + 8 , find 1 𝑦 𝑦 𝑥 2 d d .

Q14:

If 𝑦 = 𝑥 + 5 𝑥 − 5 − 𝑥 − 5 𝑥 + 5 , find d d 𝑦 𝑥 .

Q15:

Evaluate 𝑓 ′ ( 3 ) , where 𝑓 ( 𝑥 ) = 𝑥 𝑥 + 2 − 𝑥 − 3 𝑥 − 2 .

Q16:

Find 𝑔 ′ ( 𝑥 ) where 𝑔 ( 𝑥 ) = 𝑥 𝑒 2 𝑥 .

Q17:

Given that 𝑦 = 6 6 − 3 3 𝑥 3 𝑥 , find d d 𝑦 𝑥 .

Q18:

Find d d 𝑦 𝑥 , given that 𝑦 = 3 𝑒 4 + 3 𝑒 − 4 𝑥 − 4 𝑥 .

Q19:

Find the first derivative of 𝑦 = 𝑒 𝑥 + 9 𝑥 + 2 2 .

Q20:

Find d d 𝑦 𝑥 if 𝑦 = 5 + 𝑒 5 − 𝑒 3 𝑥 3 𝑥 .

Q21:

If 𝑦 = 2 𝑥 + 1 2 𝑥 − 1 3 3 , determine d d 𝑦 𝑥 .

Q22:

Find the derivative of the function 𝑦 = 𝑥 − 5 𝑥 − 2 .

Q23:

Evaluate at if .

Q24:

If 𝑦 = 𝑥 √ 𝑎 + 5 𝑥 2 2 , find 𝑥 𝑦 𝑥 9 d d .

Q25:

Calculate 𝑥 𝑦 𝑥 6 d d , given 𝑦 = 4 𝑥 − 5 8 𝑥 5 5 .
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