differentiation qustion

sorry last ones, can sonmeone help me please

1. given that y = sin3x show that d2y/dx2 = -9y

2. diffenrtitate 1+cos2x/1-cos2x

3. find value of sintheat when 7sectheta -3tantheta is a minumum

thanks!

Reply 1

Malik

12

LondonBoy

sorry last ones, can sonmeone help me please

1. given that y = sin3x show that d2y/dx2 = -9y

2. diffenrtitate 1+cos2x/1-cos2x

3. find value of sintheat when 7sectheta -3tantheta is a minumum

thanks!

y = sin3x
dy/dx= 3cos3x
d²y/dx=-9(sin3x)
.:.d²y/dx=-9y

thats all I am doing :p:

Reply 2

AlphaNumeric

10

\frac{dy}{dx} = 3\cos 3x

\frac{d^{2}y}{dx^{2}} = -9\sin 3x = -9y

y = \frac{1+\cos 2x}{1- \cos 2x}

\frac{dy}{dx} = \frac{(1-\cos 2x)(-2\sin 2x) - (1+\cos 2x)(2\sin 2x)}{(1-\cos 2x)^{2}}

Need to tidy it up yourself

y = 7 \sec \theta - 3\tan \theta

\frac{dy}{d\theta} = 7\frac{\sin x}{\cos^{2}x} - 3 \sec^{2}x = \sec^{2}x (7 \sin x - 3)

Reply 3

rachelrainbow32

2

Im gna cry i just started differentiation today! I was late for the lesson so i havent got a clue what was going on anyway n didnt get any help when i was stuck. But OMG if thats what ive got 2 do i may go n cry.
Seriously maths stresses me out.

Reply 4

damaster275

1

LondonBoy

sorry last ones, can sonmeone help me please

1. given that y = sin3x show that d2y/dx2 = -9y

2. diffenrtitate 1+cos2x/1-cos2x

3. find value of sintheat when 7sectheta -3tantheta is a minumum

thanks!

1)dy/dx = 3cos3x
d2y/dx2=-9sin3x= -9y

2)sin^2(x)=1/2(1-cos2x) and cos^2(x)=1/2(cos2x+1)
and so 1+cos2x/1-cos2x=2cos^2(x)/2sin^2(x)
=cot^2(x)
dy/dx=-cosec^2(x)
3)im too lazyyyy
damn alphanumeric beat me to it

Reply 5

Malik

12

rachelrainbow32

Im gna cry i just started differentiation today! I was late for the lesson so i havent got a clue what was going on anyway n didnt get any help when i was stuck. But OMG if thats what ive got 2 do i may go n cry.
Seriously maths stresses me out.

Dont worry thats c3,c4 stuff , the differentiation in c1 is much nicer. After while it will becomes second nature.

differentiation qustion

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