Math, asked by riya808, 1 year ago

y=log(x+√x²-a²). find dy\dx if​


Anonymous: Had u try it?

Answers

Answered by AnshPotter
0

Answer:

Step-by-step explanation:

y

d

x

=

2

x

 

Explanation:

There are 2 possible approaches.

Approach 1

differentiate using the  

chain rule

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

2

2

d

d

x

(

log

(

f

(

x

)

)

)

=

1

f

(

x

)

.

f

'

(

x

)

2

2

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−  

y

=

log

(

x

2

)

d

y

d

x

=

1

x

2

.

d

d

x

(

x

2

)

=

1

x

2

×

2

x

=

2

x

Approach 2

Using the  

law of logs

then differentiate.

Reminder    

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

2

2

log

x

n

=

n

log

x

2

2

−−−−−−−−−−−−−−−−−−  

y

=

log

x

2

=

2

log

x

d

y

d

x

=

2

×

1

x

=

2

x

Related questions

What is the derivative of  

f

(

x

)

=

log

b

(

g

(

x

)

)

?

What is the derivative of  

f

(

x

)

=

log

(

x

2

+

x

)

?

What is the derivative of  

f

(

x

)

=

log

4

(

e

x

+

3

)

?

What is the derivative of  

f

(

x

)

=

x

log

5

(

x

)

?

What is the derivative of  

f

(

x

)

=

e

4

x

log

(

1

x

)

?

What is the derivative of  

f

(

x

)

=

log

(

x

)

x

?

What is the derivative of  

f

(

x

)

=

log

2

(

cos

(

x

)

)

?

What is the derivative of  

f

(

x

)

=

log

11

(

tan

(

x

)

)

?

What is the derivative of  

f

(

x

)

=

1

+

log

3

(

x

)

?

What is the derivative of  

f

(

x

)

=

(

log

6

(

x

)

)

2

?

See all questions in Differentiating Logarithmic Functions without Base e

Impact of this question

14689 views around the world

You can reuse this answer  

Creative Commons License

iOS  

y

d

x

=

2

x

 

Explanation:

There are 2 possible approaches.

Approach 1

differentiate using the  

chain rule

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

2

2

d

d

x

(

log

(

f

(

x

)

)

)

=

1

f

(

x

)

.

f

'

(

x

)

2

2

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−  

y

=

log

(

x

2

)

d

y

d

x

=

1

x

2

.

d

d

x

(

x

2

)

=

1

x

2

×

2

x

=

2

x

Approach 2

Using the  

law of logs

then differentiate.

Reminder    

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

2

2

log

x

n

=

n

log

x

2

2

−−−−−−−−−−−−−−−−−−  

y

=

log

x

2

=

2

log

x

d

y

d

x

=

2

×

1

x

=

2

x

Related questions

What is the derivative of  

f

(

x

)

=

log

b

(

g

(

x

)

)

?

What is the derivative of  

f

(

x

)

=

log

(

x

2

+

x

)

?

What is the derivative of  

f

(

x

)

=

log

4

(

e

x

+

3

)

?

What is the derivative of  

f

(

x

)

=

x

log

5

(

x

)

?

What is the derivative of  

f

(

x

)

=

e

4

x

log

(

1

x

)

?

What is the derivative of  

f

(

x

)

=

log

(

x

)

x

?

What is the derivative of  

f

(

x

)

=

log

2

(

cos

(

x

)

)

?

What is the derivative of  

f

(

x

)

=

log

11

(

tan

(

x

)

)

?

What is the derivative of  

f

(

x

)

=

1

+

log

3

(

x

)

?

What is the derivative of  

f

(

x

)

=

(

log

6

(

x

)

)

2

?

See all questions in Differentiating Logarithmic Functions without Base e

Impact of this question

14689 views around the world

You can reuse this answer  

Creative Commons License

iOS

Answered by aquialaska
5

Answer:

\frac{\mathrm{d}\,y}{\mathrm{d} x}=\frac{1}{x+\sqrt{x^2-a^2}}\times(1+\frac{2x}{2\sqrt{x^2+a^2}})

Step-by-step explanation:

Given: y=log\,(x+\sqrt{x^2-a^2})

We need to derivate y and find dy/dx.

\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{\mathrm{d}\,log\,(x+\sqrt{x^2-a^2})}{\mathrm{d}x}

We gonna use Chain rule to find it.

=\frac{\mathrm{d}\,log\,(x+\sqrt{x^2-a^2})}{\mathrm{d}(x+\sqrt{x^2-a^2})}

=\frac{1}{x+\sqrt{x^2-a^2}}\times\frac{\mathrm{d}\,(x+\sqrt{x^2-a^2})}{\mathrm{d}x}

=\frac{1}{x+\sqrt{x^2-a^2}}\times(\frac{\mathrm{d}\,x}{\mathrm{d}x}+\frac{\mathrm{d}\sqrt{x^2+a^2}}{\mathrm{d}x})

=\frac{1}{x+\sqrt{x^2-a^2}}\times(1+\frac{1}{2\sqrt{x^2+a^2}}\times\frac{\mathrm{d}(x^2+a^2)}{\mathrm{d}x})

=\frac{1}{x+\sqrt{x^2-a^2}}\times(1+\frac{1}{2\sqrt{x^2+a^2}}\times2x)

=\frac{1}{x+\sqrt{x^2-a^2}}\times(1+\frac{2x}{2\sqrt{x^2+a^2}})

Therefore, \frac{\mathrm{d}\,y}{\mathrm{d} x}=\frac{1}{x+\sqrt{x^2-a^2}}\times(1+\frac{2x}{2\sqrt{x^2+a^2}})

Similar questions