MYTUTOR SUBJECT ANSWERS

165 views

How do you calculate the derivative of cos inverse x?

When differentiating cos inverse x, the typical method is to make  y equal to cos inverse x.

By taking cos of both sides: x = cosy.

You can then differentiate with respect to y, obtaining that: (dx/dy) = - siny

Using our knowledge of derivatives, we now know that:   (dy/dx) = -1/(siny)

From x = cosy, x^2 = (cosy)^2

                                   = 1 - (siny)^2

                   (siny)^2 = 1 - x^2

                        siny   = (1-x^2)^(1/2)

Combining this with the equation stating (dy/dx), we get:

          (dy/dx) = (-1)/((1-x^2)^(1/2))

Since y is equal to the cos inverse function, this is now equal to the derivative of cos inverse x.

Will W. GCSE Maths tutor, A Level Maths tutor, A Level Further Mathem...

4 months ago

Answered by Will, an A Level Further Mathematics tutor with MyTutor


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

89 SUBJECT SPECIALISTS

£30 /hr

Henri F.

Degree: Aerospace Engineering MEng (Masters) - Bristol University

Subjects offered: Further Mathematics , Physics+ 4 more

Further Mathematics
Physics
Maths
Electronics
.STEP.
.PAT.

“About Me I am an Aerospace Engineer currently studying my MEng at the University of Bristol. I have always been fascinated with space, spacecraft and satellites. I intend on going on to complete a PhD specialising inSpacecraft Control...”

£20 /hr

Robert F.

Degree: Mathematics (Bachelors) - Nottingham University

Subjects offered: Further Mathematics , Maths

Further Mathematics
Maths

“About Me: I am a mathematics student at the University of Nottingham. I've loved maths and science for my life and I hope that my tutorials will encourage you to do the same. I'm sociable and friendly and have tutored maths throughout ...”

MyTutor guarantee

£20 /hr

Kyle W.

Degree: Computer Science (Bachelors) - Bristol University

Subjects offered: Further Mathematics , Maths

Further Mathematics
Maths

“About me Hi my name is Kyle! I'm currently in my second year studying Computer Science at the University of Bristol. I've always had a passion for mathematics and studying computer science has gave me an appreciation for just how many...”

About the author

£22 /hr

Will W.

Degree: Mathematics (Bachelors) - Durham University

Subjects offered: Further Mathematics , Physics+ 2 more

Further Mathematics
Physics
Maths
.STEP.

“About Me: I am a Maths and Physics student at Durham University, who has always enjoyed understanding complex concepts in these subjects. I also have a passion for sharing this enjoyment. At my previous school, I ran a Maths Club. Thi...”

You may also like...

Posts by Will

How do you calculate the derivative of cos inverse x?

How do you integrate (sinx)^2?

How much work must be done on a 4.0kg frictionless trolley, to accelerate it from rest to a velocity of 5.0m/s?

Show that substituting y = xv, where v is a function of x, in the differential equation "xy(dy/dx) + y^2 − 2x^2 = 0" (with x is not equal to 0) leads to the differential equation "xv(dv/dx) + 2v^2 − 2 = 0"

Other A Level Further Mathematics questions

Given that abc = -37 + 36i; b = -2 + 3i; c = 1 + 2i, what is a?

How do you calculate the derivative of cos inverse x?

The roots of the equation z^3 + 2z^2 +3z - 4 = 0, are a, b and c . Show that a^2 + b^2 +c^2 = -2

find general solution to: x(dy/dx) + 2y = 4x^2

View A Level Further Mathematics tutors

Cookies:

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

mtw:mercury1:status:ok