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Solution - Find dy/dx if y=cos^−1(√x) - Derivative - Derivative of Inverse Function

Question

Find dy/dx if `y=cos^-1(sqrt(x))`

Solution

`Let y=cos^(-1)sqrtx`

Differentiating w.r.t x

`dy/dx=d/dx(cos^(-1)sqrtx)`

`=-1/(sqrt(1-(sqrtx)^2))d/dx(sqrtx)`

`=-1/sqrt(1-x)xx1/(2sqrtx)`

`=-(-1)/(2sqrt(x-x^2))`

Is there an error in this question or solution?

APPEARS IN

2014-2015 (March)
Question 1.4 | 2 marks
Solution for question: Find dy/dx if y=cos^−1(√x) concept: Derivative - Derivative of Inverse Function. For the courses HSC Arts, HSC Commerce, HSC Commerce (Marketing and Salesmanship), HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)
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