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How do you find the derivative of #y=pi/2sintheta-costheta#?

Answer 1

Cameron Alexander

#dy/dx=pi/2costheta+sintheta#

#"note that " pi/2" is a constant"#

#"using "color(blue)"standard derivatives"#

#• d/dx(sinx)=cosx" and " d/dx(cosx)=-sinx#

#rArrdy/dx=pi/2cosx+sinx#

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Answer 2

Cameron Alexander

To find the derivative of ( y = \frac{\pi}{2} \sin(\theta) - \cos(\theta) ):

Use the derivative rules:
- The derivative of ( \sin(\theta) ) is ( \cos(\theta) ).
- The derivative of ( \cos(\theta) ) is ( -\sin(\theta) ).
Apply these rules to the given function: [ \frac{dy}{d\theta} = \frac{\pi}{2} \cdot \cos(\theta) + \sin(\theta) ]

So, the derivative of ( y = \frac{\pi}{2} \sin(\theta) - \cos(\theta) ) with respect to ( \theta ) is ( \frac{dy}{d\theta} = \frac{\pi}{2} \cdot \cos(\theta) + \sin(\theta) ).

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Answer from HIX Tutor

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.