Differentiation questions (difficult)

Hi, how would I go about solving these? Any pointers to start me off would be great

1. Given f (x) = 4 cos x - sin^2 x, find f'(pi/2)

2. Find the coordinates of the stationary points on the curve y = sin x + cos x for 0 《 x 《 2pi and determine the nature of each point

3. I) if y = sin x (cos x)^2, find dy/dx

Ii) find the three values of x between 0 and pi radians at which dy/dx = 0

Thank you everyone!

Do you know the chain rule or the product rule?

You are going to need to differentiate for each question. Can you post some working?

Reply 2

crashMATHS

16

Original post by lolables

Hi, how would I go about solving these? Any pointers to start me off would be great

1. Given f (x) = 4 cos x - sin^2 x, find f'(pi/2)

2. Find the coordinates of the stationary points on the curve y = sin x + cos x for 0 《 x 《 2pi and determine the nature of each point

3. I) if y = sin x (cos x)^2, find dy/dx

Ii) find the three values of x between 0 and pi radians at which dy/dx = 0

Thank you everyone!

1. Given f (x) = 4 cos x - sin^2 x, find f'(pi/2) Differentiate this, and then substitute

\frac{\pi}{2}

for x. You need to have knowledge of the chain rule to solve this problem. Do you know what the chain rule is?

2. Find the coordinates of the stationary points on the curve y = sin x + cos x for 0 《 x 《 2pi and determine the nature of each point Think to yourself: what must the gradient be at a stationary point? Also, then consider how do you get the gradient at any point on this graph?

3. I) if y = sin x (cos x)^2, find dy/dx Have you ever come across the product rule? You need to use that here, and the chain rule is also part of this problem

Ii) find the three values of x between 0 and pi radians at which dy/dx = 0 After you've found the differential of

y=sinx(cosx)^2

, make it equal to zero.

I hope that is helpful! :biggrin:

I would agree with Mr M - post some working out, so we can see how much you know.

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(edited 10 years ago)

Reply 3

lolables

OP

Okay so for q1. I differentiated and got -4sin theta - 2 cos theta, and I have no idea where to go from there.

As for the other two, I don't even know where to begin

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Original post by lolables

Okay so for q1. I differentiated and got -4sin theta - 2 cos theta, and I have no idea where to go from there.

As for the other two, I don't even know where to begin

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You haven't differentiated the second term correctly. You need to use the Chain Rule or the Product Rule.

Reply 5

crashMATHS

16

Original post by lolables

Okay so for q1. I differentiated and got -4sin theta - 2 cos theta, and I have no idea where to go from there.

As for the other two, I don't even know where to begin

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f (x) = 4 cos x - sin^2 x

You've differentiated the

4cosx

correctly, but not the

-sin^2x

Like Mr M said, you need to use the chain rule here. Here's a tip to make it a little easier though:

Instead of writing

-sin^2x

as that, write it as:

-(sinx)^2

. Does that help you understand why the chain rule is needed? :biggrin:

Reply 6

lolables

OP

Original post by kingaaran

f (x) = 4 cos x - sin^2 x

You've differentiated the

4cosx

correctly, but not the

-sin^2x

Like Mr M said, you need to use the chain rule here. Here's a tip to make it a little easier though:

Instead of writing

-sin^2x

as that, write it as:

-(sinx)^2

. Does that help you understand why the chain rule is needed? :biggrin:

Thank you! So I tried again and got -4sin theta - 2 sin theta cos theta

Any better? :s

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Original post by lolables

Thank you! So I tried again and got -4sin theta - 2 sin theta cos theta

Any better? :s

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Yes that's right.

Reply 8

TenOfThem

18

Original post by lolables

Thank you! So I tried again and got -4sin theta - 2 sin theta cos theta

Any better? :s

Apart from the fact that you have changed x to theta for some reason

That is correct

Reply 9

lolables

OP

Original post by Mr M

Yes that's right.

Thank you so much! But I trued substituting the pi/2 but I keep getting the wrong answer :s the answer is supposed to be -4 but I keep getting something like -0.16...
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Reply 10

lolables

OP

Original post by TenOfThem

Apart from the fact that you have changed x to theta for some reason

That is correct

I have no idea what to do for the 2nd or 3rd question though, could you perhaps give me further guidance? Thank you so nuch

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Reply 11

davros

16

Original post by lolables

Thank you so much! But I trued substituting the pi/2 but I keep getting the wrong answer :s the answer is supposed to be -4 but I keep getting something like -0.16...
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Are you using a calculator set to degrees?!

You should know what sin(pi/2) and cos(pi/2) are without doing any calculations :smile:

Reply 12

Kvothe the Arcane

20

Original post by lolables

Hi, how would I go about solving these? Any pointers to start me off would be great

1. Given f (x) = 4 cos x - sin^2 x, find f'(pi/2)

2. Find the coordinates of the stationary points on the curve y = sin x + cos x for 0 《 x 《 2pi and determine the nature of each point

3. I) if y = sin x (cos x)^2, find dy/dx

Ii) find the three values of x between 0 and pi radians at which dy/dx = 0

Thank you everyone!

Ppl have given you advice already but use the double angle formula (sin2x=2sinxcosx) to simplify 3 then use the product rule to differentiate!

Reply 13

TenOfThem

18

Original post by lolables

I have no idea what to do for the 2nd or 3rd question though, could you perhaps give me further guidance? Thank you so nuch

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You need to differentiate for both - have you had a go

Reply 14

lolables

OP

Original post by davros

Are you using a calculator set to degrees?!

You should know what sin(pi/2) and cos(pi/2) are without doing any calculations :smile:

Oh thank you!

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Reply 15

Exon

15

Original post by lolables

Thank you so much! But I trued substituting the pi/2 but I keep getting the wrong answer :s the answer is supposed to be -4 but I keep getting something like -0.16...
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