817 views

### How do I differentiate sin^2(x)?

To differentiate sin^2(x) we must use the 'Chain Rule'. This is because we have a function of a function. We let y=sin^2(x). Then we write, 'let u=sin(x)'. This is our initial function, and we can see now that using this new notation, sin^2(x) is simply u^2. So we now write y=u^2, as this is equivalent to y=sin^2(x). To find dy/dx, we need to apply the chain rule. This states that dy/dx=dy/du x du/dx. To find dy/du we differentiate y with respect to u. Since, y=u^2, we have that dy/du=2u. To find du/dx we differentiate u with respect to x. We have that u=sin(x), so differentiating u with respect to x we have that du/dx=cos(x). Now we simply substitute the values of dy/du and du/dx into the chain rule so that we can obtain a value for dy/dx. We have that dy/dx = dy/du x du/dx, so dy/dx = 2ucos(x). However, we need the final differentiated answer to be in terms of x, as there are no 'u's in the initial expression 'sin^2(x)'. So, since u = sin(x), we subsitute in 'sin(x)' where the letter u appears in our answer for dy/dx. Therefore, instead of writing dy/dx = 2ucos(x), we write dy/dx=2sin(x)cos(x). Now we have successfully differentiated sin^2(x) with respect to x, and have written our answer correctly in terms of x.

2 years ago

Answered by Laasya, who has applied to tutor A Level Maths with MyTutor

## Still stuck? Get one-to-one help from a personally interviewed subject specialist

#### 302 SUBJECT SPECIALISTS

£20 /hr

Bukky O.

Degree: Maths with Finance (Bachelors) - Exeter University

Subjects offered:Maths, Chemistry

Maths
Chemistry

“Hi, I'm Bukky (pronounced book-ee) and my aim is to not only help your child excel in Maths but also hopefully enjoy it too”

£36 /hr

Timothy N.

Degree: Architecture and Environmental Engineering (Masters) - Nottingham University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Design & Technology
-Personal Statements-

“Hi there, I have a passion for helping students achieve, and believe that with my years of experience tutoring, we will be able to surpass the grades you want!”

£20 /hr

Degree: Electrical and Electronic Engineering (Masters) - Imperial College London University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
Electronics

“Degree: Electrical and Electronic Engineering (Masters) University: Imperial College London ”

£20 /hr

Laasya S.

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

MyTutor guarantee

### You may also like...

#### Posts by Laasya

How do I differentiate sin^2(x)?

How do I find where the stationary points of a function are?

#### Other A Level Maths questions

Factorise x^3-6x^2+9x.

How do you go about differentiating a^x functions?

A curve is described by the equation (x^2)+4xy+(y^2)+27=0. The tangent to the point P, which lies on the curve, is parallel to the x-axis. Given the x-co-ordinate of P is negative, find the co-ordinates of P.

The polynomial p(x) is given by p(x) = x^3 – 5x^2 – 8x + 48 (a) (i) Use the Factor Theorem to show that x + 3 is a factor of p(x). [2 marks] (ii) Express p(x) as a product of three linear factors. [3 marks]

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.