Question

Find the derivative of ${(\sin x)^2}$ .

Answer 1

Hint : The derivative of a function simply means that we have to find out the differentiation of the given function. So we will have to differentiate this function by $x$ . The function here given is a composite function because we will have to use the chain rule in solving it . one part of the function which is inside is a trigonometric function , the other function is the square function which is the inside function is raised to the power of $2$ . The function with the square can be differentiated by using the standard formula
$\dfrac{d}{{dx}}{x^n} = n{x^{n - 1}}$
The other function which is the trigonometric function will be solved by the standard formula for differentiation which is $\dfrac{d}{{dx}}\sin x = \cos x$ . We will use the chain rule to differentiate the function.

Complete step by step solution:
We are given the function,
${(\sin x)^2}$ And we have to find the derivative of this function which means we have to find its differentiation.
First step we will differentiate the first function which in this case is square function.
$\dfrac{d}{{dx}}{(\sin x)^2} = 2\sin x(\dfrac{d}{{dx}}\sin x)$
Then we will differentiate the inside function also by using the standard formula,
$\dfrac{d}{{dx}}{(\sin x)^2} = 2\sin x\cos x$
Thus we get our final answer. The given function was differentiated by the help of the chain rule of differentiation.
So, the correct answer is “ $\dfrac{d}{{dx}}{(\sin x)^2} = 2\sin x\cos x$ ”.

Note : Always remember that whenever we solve a differentiation the differentiation of a constant for example a number $1,2,3$ etc or a variable which is not the differentiating variable is always zero. It stays in multiplication if it is a coefficient of a variable .