Question

What is the derivative of $1 - \cos x$ ?

Answer 1

Hint : The derivative of the function is calculated by differentiating the given function by the variable that is given in the function when we differentiate we use some formulae and technique that help us to calculate the derivative of a given function. The given function is $1 - \cos x$ we can easily calculate its derivative by using the standard formula. For the first part of the question we know that the differentiation of a constant is always zero so the first part will yield zero on differentiation and for the next part we would differentiate by using the standard formula for differentiation of the trigonometric function of cosine. The formula is
$\dfrac{d}{{dx}}(\cos x) = - \sin x$

Complete step by step solution:
The given function in the question is:
$1 - \cos x$ . Since we have to find its derivative it means we have to differentiate it,
The first part is constant and will be differentiated as such, the constant part becomes zero on differentiation, and another part which is the trigonometric part is then solved using the standard formula
$\dfrac{d}{{dx}}(\cos x) = - \sin x$
The given function is
$1 - \cos x$
$\dfrac{d}{{dx}}(1 - \cos x)$ $= 0 + \sin x$
$= \sin x$
Thus the given equation given function has the derivative as,
$\sin x$
So, the correct answer is “ $\sin x$ ”.

Note : Whenever we differentiate the trigonometric function we should always remember the rule of c the rule of c is that whichever trigonometric functions begin with c always render a negative sign after differentiation so the trigonometric functions like cosine, cot, and cosec always given negative sign during the differentiation. All other trigonometric ratios give positive signs.