Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

[tex]\boxed{\large{\sf Hello\: Brainlians}}[/tex]


Find the derivative of the below function using first principle

[tex]\\ \rm\rightarrowtail f(x)=\sqrt{sinx}[/tex]

Note:-

Spams/irrelevant/incomplete/copied /wrong answers will be deleted on the spot.



Don't add incomplete answer ,solve with proper explanation and all steps .


​

Sagot :

Nepalieducation

Answer:

[tex]\frac{cosx}{2\sqrt{sinx} }[/tex]

Step-by-step explanation:

The answer is in the attachment,

View image Nepalieducation
View image Nepalieducation
Baraq

From the definition,

f¹ (x) = Lin f(x+h) - f(x)

Solution

f(x) =√sinx

f¹(x) = f(x+h) - f(x) \ h

√sin (x+h) - √sinx\h

let,

sin (x+h) = u+k

f sin x = u

k = (u+k) - u........i

= sin(x+h) - sin x........ii

h......0 = k......0...........iii

√u+k -√u\h

√u+k-√u\x. • k\h

√u+k-√u\k sin (x+h) - sinx\h

{(√u+k)²-(√u)²\k√u+k+√u}

2cos(x+h/2) sin (h/2)\h

1\√u+√u • 1 cos(x+0)

¹/2√u cos x

¹/2√sinx cos x (u= sin x)

f¹(x) = cos x/2√sinx

Therefore, the answer is cos x/2√sinx.

learn more about fraction: https://brainly.com/question/78672

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.