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Find the derivative of the below function using first principle

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

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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

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