Home > Calculus > Differentiating sin(x) from First Principles

How do you differentiate # sin (x/2)#?

Answer 1

#cos(x/2) * 1/2#

Using the chain rule; Differentiate the outer function, and then multiply it by the inner function. In this case #sin# is the outer function and #x/2# is the inner function.

The derivative of #sin(x) = cos(x)# and the derivative of #x/2 = 1/2#.

So our final answer when differentiating #sin(x/2)# with respect to x is --> #cos(x/2) * 1/2#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Isaiah Allen

To differentiate sin(x/2), you can use the chain rule of differentiation. The derivative of sin(u) with respect to x is cos(u) times the derivative of u with respect to x. In this case, u = x/2. So, the derivative of sin(x/2) is cos(x/2) times the derivative of (x/2) with respect to x, which is 1/2. Therefore, the derivative of sin(x/2) is (1/2)cos(x/2).

By signing up, you agree to our Terms of Service and Privacy Policy

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.