MYTUTOR SUBJECT ANSWERS

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. 

Laasya S. GCSE Maths tutor, A Level Maths tutor, A Level Further Math...

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”

Timothy N. A Level Design & Technology tutor, GCSE Design & Technolog...
£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

Adamos S.

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 ”

About the author

£20 /hr

Laasya S.

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

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]

View A Level Maths tutors

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

mtw:mercury1:status:ok