How do you differentiate # y= cos(pi/2x^2-pix) # using the chain rule?

1 Answer
DanT
Apr 12, 2018

#-sin(pi/2x^2-pix)*(pix-pi)#

Explanation:

First, take the derivative of the outer function, cos(x): #-sin(pi/2x^2-pix)#.
But you also have to multiply this by the derivative of what's inside, (#pi/2x^2-pix#). Do this term by term.
The derivative of #pi/2x^2# is #pi/2*2x=pix#.
The derivative of #-pix# is just #-pi#.
So the answer is #-sin(pi/2x^2-pix)*(pix-pi)#

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