IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

himani_manoj

Respected sir,

I am Himani Mishra and this for the first time I am asking subject related doubts like this on net. Please tell me that how many doubts can I ask you in one time?

In following Q?s I tried them and I got an answer also but it was not matching with the option given in the book (arihant) kindly send me solution as early as possible.

Q.1 If y = log₁₀ x + log _x 10 + log _xx + log₁₀ 10 then find dy/dx?

Q.2 If y = [4 + {4 + (4 + x²)}^1/2]^1/2 then find dy/dx?

Q.3 If y = f [(3x + 4) / (5x + 6)] and f `(x) = tan x²?

Q.4 If f `(x) = sin x + sin 4x. Cos x, then f ` (2x² + p/2) is?

The answer I got is {Cos (2x ²) - Sin 8x². Sin 2x²} and it is there in the alternatives but the correct answer mentioned by book is different. Where am I making the mistake?

Q.5 If f ` (x) = (2x² - 1)^1/2and y = f (x²), then dy/dx at x = 1, is?

My answer was 1 but answer mentioned in book is 2, how?

Thanking you,

Himani mishra

Admin

Dear Himani,

I'm afraid you can ask only one question at a time from the experts in one topic. So you need to create five such topics to ask all five questions. The expert team is an extremely busy community of highly placed people in the fields of technology and education. So we cant bombard them with so many questions at the same time

Break these questions down in 5 topics. I'll consider just the question (1) as a valid question for this thread. Rest will be removed once you have posted them as separate. If your nickels finish, refer a few friends to earn more nickels to ask.

Hope we can help you with all the issues

~forum admiinstrator

puneet

y = log₁₀ x + log _x 10 + log _xx + log₁₀ 10
= log_ex / log_e10 + log_e10/log_ex + 1 + 1

dy/dx = 1 / (x * log_e10) - log_e10/((log_ex)²* x) + 0
= 1 / (x * log_e10) - log_e10/((log_ex)²* x)

cheers !!!!!

ruhi

hi
this is the solution 4 question 3rd
y=f(3x+4/5x+6) nd f'(x)=tanx²
dy/dx=f'(3x+4/5x+6) d/dx(3x+4/5x+6)
dy/dx=tan(3x+4/5x+6)^2 * (-2/5x+6)^2
thus dy/dx= {-2/(5x+6)^2 }* {tan(3x+4/5x+6)^2}
hope my answer is correct
ruhi

ruhi

this is the answer for 5th question
y=f(x²) nd f'(x)=(2x²-1)^1/2
dy/dx=f'(x²) * (2x) = (2x⁴ -1)^1/2 * (2x)
thus dy/dx at x=1 is (2.1⁴ - 1)^1/2 * (2*1)=2
hope u get it now

polymath

Ok dude your 1st , 2nd and 5th questions have been answered. I will answer the other two.

polymath

y = [4 + {4 + (4 + x²)}^1/2]^1/2

^{Differentiating with respect to x}

^{dy/dx = d quesn/ dy}

dy/dx = 1/2*

Cant figure out how to type this sqaure roots.

I am sorry. but i will answer the other quesn as it has got no sq roots.

Admin

hmmm....

guys if you are having too much problem in anyways while using the post editor, or in any other way on the site, do send feedback to the technical team, telling the exact problem. I'm sure they will appreciate someone helping them. Just be polite and considerate with them

as they work extremely hard to ensure you guys get a good place to solve your issues. This is our place, and we have to give our suggestions to make it the best for us!

~forum administrator

himani_manoj

Thank you as you are trying to help me. I can also help you in this writing root problem.

Type your letter in M S WORD where ever you require these subscripts or you wanna put a power or any thing just click format then font and here you have all the effects subscript, superscript every thing.If you want to have alpha, beta etc. select symbols without caps lock and if you want other signs hit caps lock then have deltas and more..

hope this can help you and me also for my doubts.

Admin

you can also click on the first top button and a panel opens up for symbols and super/sub scripts. If you click on a symbol, it gets selected. If you want to make super script or subscript, select a text you wasn to make super script and press the second last button in the panel. you will get a super script. To get back to normal mode, click on the same button again.

~forum administrator

computer001

*edited*

konichiwa2x

Is this what you meant for the 3rd question?

If

and

. Find

.

konichiwa2x

For question number 4, the answer you provided is correct. The book answer is wrong.

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