The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

C3 Differentiation exam question help!

y= tan x
dy/dx = 4 + 4 tan^2 4x

show that d^2y/dx^2=qy( 1 + y^2 ), where q is a number to be determined.

Answer is 32y( 1 + y^2 )

Cannot do this question can anyone help?
Reply 1
Avatar for AndyOC
AndyOC
OP
2
...
Original post by AndyOC
y= tan x
dy/dx = 4 + 4 tan^2 4x

show that d^2y/dx^2=qy( 1 + y^2 ), where q is a number to be determined.

Answer is 32y( 1 + y^2 )

Cannot do this question can anyone help?


How did you get that dy/dx, may I ask?

The differential of tan⁡x \tan x is certainly not 4+4tan⁡2(4x) 4+4\tan^2(4x)
Reply 3
Avatar for AndyOC
AndyOC
OP
2
Original post by kingaaran
How did you get that dy/dx, may I ask?

The differential of tan⁡x \tan x is certainly not 4+4tan⁡2(4x) 4+4\tan^2(4x)


the previous question was where tan4x was expressed as sin4x/cos4x and i had to use the quotient rule
Original post by AndyOC
the previous question was where tan4x was expressed as sin4x/cos4x and i had to use the quotient rule



And are you sure that differentiating
Unparseable latex formula:

\frac{\sinx}{\cosx} = 4+\tan^2{4x}

? What is the standard differential of tanx?
(edited 8 years ago)
Reply 5
Avatar for AndyOC
AndyOC
OP
2
100% sure d/dx (sin4x/cos4x) = 4 + 4 tan^2 4x i got the same answer as the mark scheme when i did it. It's question 7 of jan 2010 aqa
Original post by AndyOC
100% sure d/dx (sin4x/cos4x) = 4 + 4 tan^2 4x i got the same answer as the mark scheme when i did it. It's question 7 of jan 2010 aqa


Ah I see - your posts differ. In your OP, you talk about differentiating y=tanx rather than 4x.

But you could simplify your result down to 4(1+tan^2x) = 4sec^2x, no?

Now, you need to prove an expression involving the second derivative, so start by finding it. What is d^2y/dx^2 ?
Reply 7
Avatar for kprime2
kprime2
20
Original post by AndyOC
y= tan x
dy/dx = 4 + 4 tan^2 4x

show that d^2y/dx^2=qy( 1 + y^2 ), where q is a number to be determined.

Answer is 32y( 1 + y^2 )

Cannot do this question can anyone help?


Screen Shot 2016-01-11 at 23.50.34.png

The fourth line was differentiation via the chain rule as follows:

Spoiler

(edited 8 years ago)

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you