Answer:
<h3>METHOD I:</h3>
(by using the first principle of differentiation)
We have the <u>"Limit definition of Derivatives"</u>:

<em>Here, f(x) = sec x, f(x+h) = sec (x+h)</em>
- <em>Substituting these in eqn. (i)</em>
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- <em>sec x can be written as 1/ cos(x)</em>
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- <em>By Cosines sum to product formula, i.e.,</em>

<em>=> cos(x) - cos(x+h) = -2sin{(x+x+h)/2}sin{(x-x-h)/2}</em>

- <em>I shifted a 2 from the first limit to the second limit, since the limits ar ein multiplication this transmission doesn't affect the result</em>

- <em>2/ h can also be written as 1/(h/ 2)</em>

- <em>We have limₓ→₀ (sin x) / x = 1. </em>
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- <em>h→0 means h/ 2→0</em>
<em>Substituting 0 for h and h/ 2</em>
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- <em>sin x/ cos x is tan x whereas 1/ cos (x) is sec (x)</em>

Hence, we got

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
<h3>METHOD II:</h3>
(by using other standard derivatives)

- sec x can also be written as (cos x)⁻¹
We have a standard derivative for variables in x raised to an exponent:

Therefore,

- Any base with negative exponent is equal to its reciprocal with same positive exponent

The process of differentiating doesn't just end here. It follows chain mechanism, I.e.,
<em>while calculating the derivative of a function that itself contains a function, the derivatives of all the inner functions are multiplied to that of the exterior to get to the final result</em>.
- The inner function that remains is cos x whose derivative is -sin x.

- cos²x can also be written as (cos x).(cos x)

- <u>sin x/ cos x</u> is tan x, while <u>1/ cos x</u> is sec x

= sec x. tan x
<h3>Hence, Proved!</h3>
Answer:
P = 1/5 = 0.20 = (20%)
Step-by-step explanation:
there are 12 horses and 8 cows, in total there are 20 animals
of which 4 horses are brown
Then

Hope this helps
I dont know i wish i could help ask me anytime with any thing else
Answer: 349 square units
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Work Shown:
- L = 5.5 = length
- W = 5 = width
- H = 14 = height
SA = surface area of rectangular prism
SA = 2*(L*W + L*H + W*H)
SA = 2*(5.5*5 + 5.5*14 + 5*14)
SA = 2*(27.5 + 77 + 70)
SA = 2*(174.5)
SA = 349
The surface area is 349 square units.
Answer:
Step-by-step explanation:
the dot is on the 32 and the line is the 3rd line