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In this lesson, we will learn how to use the fundamental theorem of calculus to find the derivative of a function.

Q1:

Use the fundamental theorem of calculus to find the derivative of the function β ( π’ ) = οΈ β 3 π‘ 4 π‘ + 2 π‘ ο οͺ d .

Q2:

Given that οΈ π ( π₯ ) π₯ = π₯ β 7 π₯ β π₯ + 9 + d C 3 2 , find π β² ( 1 ) .

Q3:

Use the Fundamental Theorem of Calculus to find the derivative of the function π ( π¦ ) = οΈ 3 π‘ 2 π‘ π‘ 5 π¦ 2 s i n d .

Q4:

Find the derivative of the function π ( π₯ ) = οΈ 5 π‘ π‘ π‘ 1 + π₯ 1 β 2 π₯ s i n d .

Q5:

Find the derivative of the function π¦ ( π₯ ) = οΈ ( 1 β π£ ) π£ 4 π₯ 3 π₯ s i n c o s l n d .

Q6:

Suppose that π is a function on the interval [ π , π ] and we are able to define πΉ by πΉ ( π₯ ) = οΈ π ( π‘ ) π‘ ο οΊ d . We find that πΉ is NOT differentiable on ( π , π ) . What can we conclude?

Q7:

The figure shows the graph of the function οΈ π ( π‘ ) π‘ . π₯ 0 d

Which of the following is the graph of π¦ = π ( π₯ ) ?

Q8:

Use the Fundamental Theorem of Calculus to find the derivative of the function π¦ = οΈ 2 π‘ 2 + π‘ π‘ 5 π₯ + 3 4 5 d .

Q9:

Use the Fundamental Theorem of Calculus to find the derivative of the function π¦ = οΈ 5 ( 5 π ) π π₯ 2 2 4 c o s d .

Q10:

Use the fundamental theorem of calculus to find the derivative of the function π ( π₯ ) = οΈ οΉ 1 + π‘ ο π‘ ο ο© ο« l n d .

Q11:

Use the Fundamental Theorem of Calculus to find the derivative of the function π ( π ) = οΈ οΉ 3 π‘ β 4 π‘ ο π‘ π 1 3 5 4 d .

Q12:

Use the Fundamental Theorem of Calculus to find the derivative of the function πΉ ( π₯ ) = οΈ β 2 β 3 π‘ π‘ 4 π₯ s e c d .

Q13:

Use the Fundamental Theorem of Calculus to find the derivative of the function π ( π₯ ) = οΈ β 2 π‘ π‘ π₯ 2 4 d .

Q14:

Find the derivative of the function π ( π₯ ) = οΈ π’ β 3 π’ + 5 π’ 4 π₯ 3 π₯ 2 2 d .

Q15:

Find the derivative of the function πΉ ( π₯ ) = οΈ 2 π π‘ 2 π₯ 5 π₯ π‘ 2 2 d .

Q16:

Given that πΉ ( π₯ ) = οΈ π‘ π‘ 4 π₯ β π₯ β 1 t a n d , find πΉ β² ( π₯ ) .

Q17:

Let π¦ = οΈ β 2 + 5 π‘ π‘ ο¨ ο¨ ο ο¨ s i n d . Use the Fundamental Theorem of Calculus to find π¦ β² .

Q18:

Use the Fundamental Theorem of Calculus to find the derivative of the function π¦ = οΈ 3 π 5 π π π 3 β 5 π₯ t a n d .

Q19:

Use the Fundamental Theorem of Calculus to find the derivative of the function β ( π₯ ) = οΈ 3 π§ π§ + 2 π§ β π₯ 4 2 4 d .

Q20:

Given that π ( π₯ ) = οΈ οΉ 8 π₯ β 5 π₯ + 4 ο π₯ 2 d , find d d π π₯ .

Q21:

Use the Fundamental Theorem of Calculus to find the derivative of the function β ( π₯ ) = οΈ β π‘ π‘ π 2 5 π₯ l n d .

Q22:

Given that οΈ π ( π₯ ) π₯ = 3 π₯ + π₯ β 8 π₯ + 5 + d C 3 2 , find π β² ( β 1 ) .

Q23:

Use the Fundamental Theorem of Calculus to find the derivative of the function π ( π¦ ) = οΈ β π‘ 3 π‘ π‘ 1 π¦ 2 s i n d .

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