# What is the derivative of f(theta)=arcsin(sqrt(sin(9theta)))?

##(df)/(d theta) = 9/2 * cos(9theta)/(sqrt(sin(9theta)) * sqrt(1 – sin(9theta)))##

Don't use plagiarized sources. Get Your Custom Essay on
What is the derivative of f(theta)=arcsin(sqrt(sin(9theta)))?
Just from \$13/Page

You can differentiate this function by using , provided that you don’t know what the derivative of ##arcsin(x)## is.

You will also need to use the and the fact that

##d/dx(sinx) = cosx##

##f(theta) = arcsin(sqrt(sin(9theta)))##

is equivalent to

##sin(f) = sqrt(sin(9theta)) ” “color(orange)((1))##

Differentiate both sides with respect to ##theta##

##d/(d theta)(sin(f)) = d/(d theta)sqrt(sin(9theta))##

Focus on finding ##d/(d theta)sqrt(sin(9theta))## first. Use the twice to get

##d/(d theta)sqrt(sin(9theta)) = 1/2sin(9theta)^(-1/2) * cos(9theta) * 9##

##d/(d theta)sqrt(sin(9theta)) = 9/2 sin(9theta)^(-1/2) * cos(9theta)##

Take this back to your target derivative to get

##cos(f) * (df)/(d theta) = 9/2sin(9theta)^(-1/2) * cos(9theta)##

Isolate ##(df)/(d theta)## on one side

##(df)/(d theta) = 9/2 * (sin(9theta)^(-1/2) * cos(9theta))/cos(y)##

Use the trigonometric identity

##color(blue)(sin^2x + cos^2x = 1)##

to write ##cosx## as a function of ##sinx##

##cos^2x = 1 – sin^2x implies cosx = sqrt(1- sin^2x)##

This will get you

##(df)/(d theta) = 9/2 * (sin(9theta)^(-1/2) * cos(9theta))/sqrt(1-sin^2(y))##

Finally, use equation ##color(orange)((1))## to get

##(df)/(d theta) = 9/2 * (sin(9theta)^(-1/2) * cos(9theta))/sqrt(1- (sqrt(sin(9theta)))^2)##

This is equivalent to

##(df)/(d theta) = color(green)(9/2 * cos(9theta)/(sqrt(sin(9theta)) * sqrt(1 – sin(9theta))))##

## Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
\$26
The price is based on these factors:
Number of pages
Urgency
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)

# Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

### Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

### Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

### Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.