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Differentiation homework help

poppydoodle

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Completely confused, any help appreciated

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Reply 1

username3249896

Original post by poppydoodle

Completely confused, any help appreciated

To differentiate use the product rule

\dfrac{d}{dx} (uv) = v \dfrac{du}{dx} + u \dfrac{dv}{dx}

where u = cos x and v = e^2x.

For (a) set dy/dx =0

For (b), calculate the gradient at x=0 and the y-value at x=0. Then find the equation of the tangent

(edited 6 years ago)

Reply 2

RDKGames

Study Forum Helper

Original post by poppydoodle

Completely confused, any help appreciated

Have you covered the product rule?

Reply 3

poppydoodle

dy/dx = cos(x) 2e^2x - e^2x sin(x)

Is this right?

Reply 4

RDKGames

Study Forum Helper

Original post by poppydoodle

dy/dx = cos(x) 2e^2x - e^2x sin(x)

Is this right?

Yes.

Do you know how to carry on with the question?

Reply 5

poppydoodle

Original post by RDKGames

Yes.

Do you know how to carry on with the question?

I know you set it equal to 0 but I don’t know how to solve it

Reply 6

thekidwhogames

dy/dx = cos(x) 2e^2x - e^2x sin(x)

Factor e^2x.

Reply 7

RDKGames

Study Forum Helper

Original post by poppydoodle

I know you set it equal to 0 but I don’t know how to solve it

You do not need to solve it.

First, you can divide through by

e^{2x}

because it's never equal to 0.
Then try to obtain

\tan(x)

one side and hence show the equality in question.

2cosx-sinx=0 ?

Original post by poppydoodle

2cosx-sinx=0 ?

Yes but as I said, rearrange to get tan(x)

Reply 10

poppydoodle

Original post by RDKGames

Yes but as I said, rearrange to get tan(x)

I don’t understand how to do that

Reply 11

simon0

Hint:

\displaystyle \tan(x) = \frac{\sin(x)}{\cos(x)}.

Reply 12

RDKGames

Study Forum Helper

Original post by poppydoodle

I don’t understand how to do that

Well, look how tan(x) is defined in terms of sin(x) and cos(x), then think about what needs to happen to your equation if you want to obtain tan(x) in there.

Reply 13

poppydoodle

Ahhh ok got it thank you :smile:

For B do you set dy/dx to 0

Reply 14

RDKGames

Study Forum Helper

Original post by poppydoodle

Ahhh ok got it thank you :smile:

For B do you set dy/dx to 0

No because dy/dx=0 only for stationary points. Here is it asking you to find an equation of a tangent line through a point whose x-coordinate is

x=0

. So, you need to determine the gradient

x=0

, and also find the y-coordinate of this point before constructing the equation.

Reply 15

poppydoodle

Could you explain it more? Not sure what you mean

Reply 16

RDKGames

Study Forum Helper

Original post by poppydoodle

Could you explain it more? Not sure what you mean

You have a curve, there is a point with an x-coordinate equal to 0 on it, and you want to find the tangent line to the curve through it.

In C1 you must've done problems where you find a tangent line to a curve through a point by finding the gradient of the curve at that point and constructing the equation of the tangent line. Same idea here.