MYTUTOR SUBJECT ANSWERS

254 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...

6 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

83 SUBJECT SPECIALISTS

£20 /hr

Mark H.

Degree: Mathematics MMath (Masters) - Manchester University

Subjects offered:Further Mathematics , Physics+ 1 more

Further Mathematics
Physics
Maths

“Hello there, I'm Mark and I study Mathematics at the University of Manchester! Let me help you achieve your best! ”

£20 /hr

Sam A.

Degree: Mathematics (Bachelors) - York University

Subjects offered:Further Mathematics , Maths+ 1 more

Further Mathematics
Maths
Biology

“An enthusiastic and engaging undergrad mathematician (University of York, MMath), whose lessons are focused for the student, and never the teacher.”

Roma V. A Level Maths tutor, 13 Plus  Maths tutor, GCSE Maths tutor, ...
£26 /hr

Roma V.

Degree: Mathematics, Operational Research, Statistics and Economics (Bachelors) - Warwick University

Subjects offered:Further Mathematics , Maths+ 1 more

Further Mathematics
Maths
Economics

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

About the author

£30 /hr

Will W.

Degree: Mathematics (Bachelors) - Durham University

Subjects offered:Further Mathematics , Physics+ 2 more

Further Mathematics
Physics
Maths
.STEP.

“Hi, I'm Will. I study Maths and Physics and really enjoy talking about them. I am patient and caring, so will take the time to refine a student’s understanding.”

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

Integrate cos(4x)sin(x)

Find the complex number z such that 5iz+3z* +16 = 8i. Give your answer in the form a + bi, where a and b are real numbers.

How do you find the cube root of z = 1 + i?

How do I solve a simultaneous equation with more unknowns than equations?

View A Level Further Mathematics 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