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In this lesson, we will learn how to calculate the derivatives for parametric functions, such as first and second derivatives.

Q1:

Given that π₯ = 3 π‘ + 1 3 and π¦ = 5 π‘ β π‘ 2 , find d d π¦ π₯ .

Q2:

Given that π₯ = 4 π‘ + 1 2 and π¦ = 4 π‘ + 5 π‘ 2 , find d d π¦ π₯ .

Q3:

Given that π₯ = 3 π 5 π‘ and π¦ = π‘ π β 5 π‘ , find d d π¦ π₯ .

Q4:

Given that π₯ = 5 π‘ β 4 π‘ l n and π¦ = 4 π‘ + 5 3 π‘ l n , find d d π¦ π₯ .

Q5:

Given that π₯ = π‘ c o s and π¦ = 2 π‘ s i n , find d d π¦ π₯ .

Q6:

Given that π₯ = π‘ c o s and π¦ = 2 π‘ s i n , find d d 2 2 π¦ π₯ .

Q7:

Given that π₯ = 2 π‘ 4 + π‘ and π¦ = β 4 + π‘ , find d d π¦ π₯ .

Q8:

Given that π₯ = 3 π‘ + 1 2 and π¦ = 3 π‘ + 5 π‘ 2 , find d d 2 2 π¦ π₯ .

Q9:

Given that π₯ = π‘ β π‘ l n and π¦ = π‘ + π‘ l n , find d d 2 2 π¦ π₯ .

Q10:

Given that π¦ = β 4 π₯ β 5 2 and π§ = 5 π₯ + 9 2 , determine π¦ ο½ π¦ π₯ ο + π§ π₯ d d d d .

Q11:

Given that π₯ = β β π‘ + 5 and π¦ = β 2 π‘ + 1 , find d d π¦ π₯ at π‘ = 0 .

Q12:

If π¦ = π₯ β 5 + π₯ 2 and π§ = β 5 + π₯ 5 π₯ 2 , find 5 π§ π¦ π₯ + π§ π₯ 2 d d d d .

Q13:

Given that π₯ = 5 π‘ π π‘ and π¦ = 3 π‘ + 4 π‘ s i n , find d d π¦ π₯ .

Q14:

Find the derivative of 7 π₯ + 4 π₯ s i n with respect to c o s π₯ + 1 at π₯ = π 6 .

Q15:

Find d d π¦ π₯ at π = π 3 , given π₯ = 5 π + 7 2 π c o s c o s and π¦ = 7 π + 4 2 π s i n s i n .

Q16:

Find d d π¦ π₯ at π = 1 6 , given that π₯ = β 9 2 π π s i n and π¦ = β 4 2 π π c o s .

Q17:

By using parametric differentiation, determine the derivative of 5 π₯ + π₯ β 2 3 2 with respect to 4 π₯ + 8 2 .

Q18:

Given that π¦ = β 7 π‘ + 8 3 , and π§ = β 7 π‘ + 3 2 , find the rate of the change of π¦ with respect to π§ .

Q19:

Find the derivative of π₯ β 6 π₯ β 9 with respect to β 8 π₯ + 1 at π₯ = 3 .

Q20:

Find the rate of change of ( π₯ + 2 ) ( π₯ + 7 ) with respect to π₯ β 2 π₯ β 7 .

Q21:

Find the rate of change of l n οΉ β 3 π₯ β 1 ο 4 with respect to οΉ β 6 π₯ β 5 ο 2 at π₯ = 1 .

Q22:

Find the equation of the tangent to the curve π₯ = 5 π s e c and π¦ = 5 π t a n at π = π 6 .

Q23:

Suppose π₯ = β 3 5 π + 1 3 s e c 2 and π¦ = β 3 5 π β 1 4 t a n . Find d d π¦ π₯ when π = π 4 .

Q24:

If π₯ = β 8 π‘ β 8 5 and π¦ = β π‘ 5 6 , find d d π¦ π₯ at π‘ = 1 .

Q25:

A curve has parametric equations π₯ = 7 π + 5 π + π + 4 3 2 and π¦ = 6 π β 6 π β 8 2 . Find π for which the tangent is horizontal.

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