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

What is the derivative of #sin (x/2)#?

Answer 1

#1/2 cos (x/2)#

if you know that #d/dx sin x = cos x# then you can use the chain rule so by letting #u = x / 2# you have #d/(du) sin u = cos u#

and #(du)/dx = (d)/dx (x/2)= 1/2#

#so d/{du} (sin u) \times (du)/(dx) = cos u \times 1/2 = 1/2 cos (x/2)#

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

Answer 2

Aurora Alvarado

The derivative of ( \sin\left(\frac{x}{2}\right) ) is ( \frac{1}{2}\cos\left(\frac{x}{2}\right) ).

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

Answer 3

Paisley Johnson

The derivative of 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 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.