C3 Differentiation question urgent help! Watch

Mr Tall
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Show that y=xsin(x) has a stationary point when x=-tan(x)


how do i go about this? I know i use the product rule but do I substitute -tanx into y=xsinx and then differentiate or what? then what do i do?

thanks!
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Mike_123
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(Original post by Mr Tall)
Show that y=xsin(x) has a stationary point when x=-tan(x)


how do i go about this? I know i use the product rule but do I substitute -tanx into y=xsinx and then differentiate or what? then what do i do?

thanks!
product rule states that if y = uv then dy/dx = uv' + vu'

so let u = x and v = sinx

the order doesn't actually matter.
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Mr Tall
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(Original post by Mike_123)
product rule states that if y = uv then dy/dx = uv' + vu'

so let u = x and v = sinx

the order doesn't actually matter.
but how do i show it has a stationary point when x=-tanx
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TenOfThem
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(Original post by Mr Tall)
Show that y=xsin(x) has a stationary point when x=-tan(x)


how do i go about this? I know i use the product rule but do I substitute -tanx into y=xsinx and then differentiate or what? then what do i do?

thanks!
If the question said "find the stationary point of y=xSinx" what would you do
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Mike_123
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(Original post by Mr Tall)
but how do i show it has a stationary point when x=-tanx
A stationary point means the first derivative is 0.
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Mr Tall
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(Original post by TenOfThem)
If the question said "find the stationary point of y=xSinx" what would you do
yeap im aware that at a stationary point dy/dx=0

would i sub -tanx into y=xsinx and then show that it equals zero or what?

thanks
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TenOfThem
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(Original post by Mr Tall)
yeap im aware that at a stationary point dy/dx=0

would i sub -tanx into y=xsinx and then show that it equals zero or what?

thanks
Why have you not answered the question that I asked?
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WK_Of_Angmar
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A stationary point of a function is a point at which the gradient of the curve of that function is 0. Therefore, you need to differentiate the function using the product rule, and then equate the answer to 0. Shuffle the terms around to get the equation that was given to you.
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TenOfThem
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(Original post by WK_Of_Angmar)
...
DO you understand why the forum rules ask us not to give full solutions?
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WK_Of_Angmar
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(Original post by TenOfThem)
DO you understand why the forum rules ask us not to give full solutions?
Sorry, I forgot. Edited answer.
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TenOfThem
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(Original post by WK_Of_Angmar)
Sorry, I forgot. Edited answer.
Fair enough
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charlesturner8
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(Original post by Mr Tall)
Show that y=xsin(x) has a stationary point when x=-tan(x)


how do i go about this? I know i use the product rule but do I substitute -tanx into y=xsinx and then differentiate or what? then what do i do?

thanks!
Yes you do and make it equal to zero, assuming you have a value for X
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TheSK00T3R
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You could sub -tanx in, I don't think it would get you anywhere.
Start off differentiating y=xsinx as you usually would, and equate it to zero.
Then factorise your answer.
This will involve utilising trig identities.
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Mike_123
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(Original post by Mr Tall)
yeap im aware that at a stationary point dy/dx=0

would i sub -tanx into y=xsinx and then show that it equals zero or what?

thanks
You're not substituting anything. You're working towards that answer. It should become obvious if you've done it correctly.
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TenOfThem
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(Original post by charlesturner8)
Yes you do and make it equal to zero, assuming you have a value for X
No
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