Find f-0 for fx-x-x2-a2-a2logx-x2-a2

The correct option is A 2aGiven, f(x)=x√(x^2+a^2)+a^2log(x+√(x^2+a^2)) .Now, #160; f'(x)=√(x^2+a^2)+x.2x2√(x^2+a^2)+a^2.1+2x2√(x^2+a^2)(x+√(x^2+a^2)) ...

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Byju's Answer

Standard XII

Mathematics

Standard Logarithm

Find f'0 fo...

Question

Find $f^{'} (0)$ for $f (x) = x \sqrt{x^{2} + a^{2}} + a^{2} log (x + \sqrt{x^{2} + a^{2}})$

-2a

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-a

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Solution

The correct option is A 2a
Given,
$f (x) = x \sqrt{x^{2} + a^{2}} + a^{2} log (x + \sqrt{x^{2} + a^{2}})$ .
Now,
$f^{'} (x) = \sqrt{x^{2} + a^{2}} + x . \frac{2 x}{2 \sqrt{x^{2} + a^{2}}} + a^{2} . \frac{1 + \frac{2 x}{2 \sqrt{x^{2} + a^{2}}}}{(x + \sqrt{x^{2} + a^{2}})}$ .
Now,
$f^{'} (0) = a + 0 + a^{2} . \frac{1}{a}$
or, $f^{'} (0) = 2 a$ .

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Similar questions

Q. If

y = x \sqrt{a^{2} + x^{2}} + a^{2} log (x + \sqrt{a^{2} + x^{2}})

then

\frac{d y}{d x} = 2 \sqrt{a^{2} + x^{2}}

Q. State True or False:

y = x \sqrt{a^{2} + x^{2}} + a^{2} log (x + \sqrt{a^{2} + x^{2}}) t h e n \frac{d y}{d x} = 2 \sqrt{a^{2} + x^{2}}

Q. If

f (x) = \frac{a + \sqrt{a^{2} - x^{2}} + x}{\sqrt{a^{2} - x^{2}} + a - x}

where

a > 0

and

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, then

f^{^{'}} (0)

has the value equal to

Q.
If

f (x) = \frac{\sqrt{a^{2} - a x + x^{2}} - \sqrt{a^{2} + a x + x^{2}}}{\sqrt{a + x} - \sqrt{a - x}}

is continuous at

x = 0

then

f (0) =

Q. Verify Rolle's theorem for

f (x) = x \sqrt{a^{2} - x^{2}}

[0, a]

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Find f′(0) for f(x)=x√x2+a2+a2log(x+√x2+a2)

The correct option is A 2aGiven,f(x)=x√x2+a2+a2log(x+√x2+a2).Now, f′(x)=√x2+a2+x.2x2√x2+a2+a2.1+2x2√x2+a2(x+√x2+a2).Now, f′(0)=a+0+a2.1aor, f′(0)=2a.

Find $f^{'} (0)$ for $f (x) = x \sqrt{x^{2} + a^{2}} + a^{2} log (x + \sqrt{x^{2} + a^{2}})$