Question

derivative of (sinx)2
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Answer 1

Answer:

f(x) = (sin x)2 can be written as f(u) = u2 where u = sin x. The Chain Rule states that to differentiate a composite function we differentiate the outer function and multiply by the derivative of the inner function. We can use the rules cos x = sin ( /2– x) and sin x = cos( /2 – x) to find the derivative of cos x.

Answer 2

Full Answer on the Above:

Question:--

[Note: See the answer carefully]

Derivative of (sinx)2.

Step-by-step explanation:

Solution:

d/dx sinx = cos x

Explanation:

By definition of the derivative:

f' (x) = lim f(x + h) - f(x)/h

h -› 0

So with f(x) = sin x we have:

f' (x) = lim sin(x + h) - sin x/h

h -› 0

Using sin (A + B) = sin A cos B + sin B cos A. we get,

F' (x) = lim sin x cos h + sin h cos x - sin x/h

h--›0

= lim sin x(cos h - 1) + sin h cos x/h

h--›0.

Hence,

d/dx sin x = cos x.