IXL - Chain rule (Calculus practice)

Values of

(

)

(

)

and their derivatives are given in the tables below.

x	f ( x )	f ′ ( x )
0	1	– 6
2	– 6	– 1
5	– 8	4

x	g ( x )	g ′ ( x )
– 9	9	3
– 2	– 3	– 6
0	5	2

Find

(

∘

)

′

(

)

ref_doc_title.

Learn with an example

question

Values of

(

)

(

)

and their derivatives are given in the tables below.

x	f ( x )	f ′ ( x )
– 8	– 6	1
– 5	0	5
2	– 4	3

x	g ( x )	g ′ ( x )
– 5	2	– 7
0	– 8	– 9
5	1	5

Find

(

∘

)

′

(

–

)

key idea

The chain rule can be used to differentiate a composition of functions, like

(

∘

)

(

)

(

)

The chain rules states that if

(

)

is differentiable at

and

(

)

is differentiable at

(

)

then

(

∘

)

(

)

is differentiable at

(

∘

)

′

(

)

′

(

)

′

(

)

solution

Apply the chain rule to rewrite

(

∘

)

′

(

–

)

(

∘

)

′

(

–

)

′

(

–

)

′

(

–

)

Use the tables to find

′

(

–

)

and

′

(

–

)

Then, multiply them to calculate

(

∘

)

′

(

–

)

Find

′

(

–

)

To find

′

(

–

)

first find

(

–

)

Then, find the value of

′

(

)

(

–

)

x	f ( x )	f ′ ( x )
– 8	– 6	1
– 5	0	5
2	– 4	3

x	g ( x )	g ′ ( x )
– 5	2	– 7
0	– 8	– 9
5	1	5

From the tables,

(

–

)

and

′

(

)

–

So,

′

(

–

)

–

Find

′

(

–

)

x	f ( x )	f ′ ( x )
– 8	– 6	1
– 5	0	5
2	– 4	3

From the table,

′

(

–

)

Find

(

∘

)

′

(

–

)

Multiply

′

(

–

)

and

′

(

–

)

to calculate

(

∘

)

′

(

–

)

(

∘

)

′

(

–

)

′

(

–

)

′

(

–

)

–

So,

(

∘

)

′

(

–

)

–

Looking for more? Try this:

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