What is the implicit derivative of #25=sin(xy)/x-3xy#?
Long time since tried this but I am having a go!
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By working step-wise taking derivatives of individual components you should end up with
This is complex so check carefully before assuming what follows is valid:
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To find the implicit derivative of ( 25 = \frac{\sin(xy)}{x} - 3xy ), differentiate both sides of the equation with respect to ( x ) using the product rule and chain rule. The implicit derivative will be:
[ \frac{d}{dx} (25) = \frac{d}{dx} \left(\frac{\sin(xy)}{x}\right) - \frac{d}{dx} (3xy) ]
[ 0 = \frac{y\cos(xy)}{x} - \frac{\sin(xy)}{x^2} - 3y - 3x\frac{dy}{dx} ]
[ \frac{dy}{dx} = \frac{\sin(xy)}{x^2} - \frac{y\cos(xy)}{x} - 3y ]
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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