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How do you differentiate #cos(pi*x^2)#?

Answer 1

Luke Alvarez

Derivative of #cos(pi*x^2)# is #-2pixsin(pi*x^2)#

We can use Chain rule here. Let #f(x)=cos(pi*x^2)#. Then we can write it as

#f(x)=cosg(x)#, where #g(x)=pi*x^2#.

Then #(df)/(dx)=(df)/(dg)xx(dg)/(dx)#

= #-sin(pi*x^2)xxpixx2x#

= #-2pixsin(pi*x^2)#

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Answer 2

Scarlett Allison

To differentiate cos(pix^2), you can use the chain rule. The derivative is -2pixsin(pi*x^2).

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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.

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