Home > Calculus > Intuitive Approach to the derivative of y=sin(x)

What is the derivative of #sin^2x+cos^2x#?

Answer 1

We have:

# f(x) = sin^2x + cos^2x #

We can differentiate using the chain rule to get:

# f'(x) = 2sinxd/dx(sinx) + 2cosxd/dx(cosx) # # " " = 2sinxcosx + 2cosx(-sinx) # # " " = 2sinxcosx - 2sinxcosx # # " " = 0 \ \ \ # QED

However, it really should be clear that the above calculation was completely unnecessary and the result is obvious.

A fundamental trigonometric identity is:

# sin^2A+cos^2A -=1 \ \ \ AA A in RR#

Hence we have:

# f(x) = 1 \ \ \ AA x in RR#

ie, #f(x)# is a constant function, and the derivative of constant is zero.

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Answer 2

Evelyn Agard

The derivative of ( \sin^2(x) + \cos^2(x) ) is 0.

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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.