Math, asked by vijaychau9008, 2 months ago

y=cos(x^2-3x)
y = cos(x2 - 3x)

Answers

Answered by pragyakumari338
0

Answer:

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Answered by prachi01238
0

Answer:

The chain rule is useful whenever you have nested functions, meaning something that looks like this;

y

=

f

(

g

(

x

)

)

The chain rule tells us;

d

d

x

f

(

g

(

x

)

)

=

f

'

(

g

(

x

)

)

g

'

(

x

)

In this case, we have three nested functions;

y

=

f

(

g

(

h

(

x

)

)

)

Where;

f

=

g

2

g

=

cos

(

h

)

h

=

x

2

3

x

Plug each function into the one above it to see that you get the original function. To solve, use the chain rule first on

f

.

f

'

(

g

)

=

2

g

g

'

Now we use the chain rule again to solve for

g

'

.

g

'

(

h

)

=

sin

(

h

)

h

'

And when we solve for

h

'

via power rule;

h

'

(

x

)

=

2

x

3

Now just plug in

f

,

f

'

,

g

,

g

'

,

h

, and

h

'

and you get;

f

'

(

x

)

=

2

cos

(

x

2

3

x

)

(

sin

(

x

2

3

x

)

(

2

x

3

)

)

=

(

6

4

x

)

sin

(

x

2

3

)

cos

(

x

2

3

)

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