Differentiation... (1 Viewer)

[Norma.Jean]

Differentiate:
x(7-4x)^ 9

Thats to the power of nine if you couldn't understand it....but anywho help would be appreciated

 

[Norma.Jean]

so do you mean

d/dx[x^9 . (7-4x)]?

fixed it up

 

[PC]

Use the product rule.

d/dx[x⁹(7 – 4x)]
= x⁹.d/dx[7 – 4x] + (7 – 4x).d/dx[x⁹]
= x⁹.(–4) + (7 – 4x).9x⁸
= –4x⁹ + 9x⁸(7 – 4x)
= –4x⁹ + 63x⁸ – 36x⁹
= 63x⁸ – 40x⁹

 

[Norma.Jean]

Yes i got that far as well but the answer is
(7-4x)^8(7-40x)

 

[lyounamu]

Yes i got that far as well but the answer is
(7-4x)^8(7-40x)

Just expand and simplify:

(7-4x)^9 - 36x.(7-4x)^8 = (7-4x)^8 ((7-4x) - 36x)
= *7-4x)^8 (7-40x)

 

[bored of sc]

Differentiate:
x(7-4x)^ 9

Thats to the power of nine if you couldn't understand it....but anywho help would be appreciated

Product rule is dy/dx = uv' + vu'

So y = x(7-4x)⁹

u = x, v = (7-4x)⁹ u' = differentiation of u, v' = differentiation of v

dy/dx = x.9(7-4x)⁸.-4 + (7-4x)⁹.1 <--- used the product rule, don't forget to use function of a function rule when differentiating (7-4x)⁹

= -36x(7-4x)⁸ + (7-4x)⁹ <--- multiplied

= (7-4x)⁸(-36x+(7-4x)) <------ took out common factor of (7-4x)⁸

= (7-4x)⁸(7-40x) <------- added brackets to form second factor

 

[Annum]

Hey Guys can someone please help me with this equation pleaase
I have to determine the nature of the stationary points: the equation is

y= x^3/3 - 2x^2 + 3x +4

I also had another question regarding maximum and minimum turning points. Is maximum always lower than 0 and minimum always higher than 0?
Thankyou soo much

 

[Carrotsticks]

There are 3 ways of determining the stationary point:

1. Table method

2. Double derivative

3. Cheap method

I'll explain them when I get back, unless somebody does it before me.

 

[SpiralFlex]

At

 

[Annum]

Thankyou, the question is asking to determine it using double derivative

 

[SpiralFlex]

There are 3 ways of determining the stationary point:

1. Table method

2. Double derivative

3. Cheap method

I'll explain them when I get back, unless somebody does it before me.

Lol what's the cheap method?

 

[Annum]

At

Thankyou so much for this

 

[Bored_of_HSC]

Lol what's the cheap method?

Hmm i think he means using values very close to the stationary point and seeing wheither they're higher or lower than the point.

That'd work in my opinion (though probably more tedious).

 

[SpiralFlex]

Hmm i think he means using values very close to the stationary point and seeing wheither they're higher or lower than the point.

That'd work in my opinion (though probably more tedious).

That's the tabular method. The only cheap method I can think of is doing it in your head since this curve is common.

 

[Bored_of_HSC]

That's tabular.

I think by tabular he meant first derivative.

 

[SpiralFlex]

I think by tabular he meant first derivative.

Yes you're actually testing either sides when using the first derivative.

I am betting the cheap method is in your head.

 

[Peeik]

maybe the cheap method is to wolfram it?

 

[SpiralFlex]

Okay. I'll sleep for 2 hours when I get back hopefully I will know what the "cheap" method is.

 

[Bored_of_HSC]

Yes you're actually testing either sides when using the first derivative.

I am betting the cheap method is in your head.

Nah umm but what i meant was. You could still use the actual f(x) graph to test it either way.

Either way we'll see what he means when he comes back.

 

[Bored_of_HSC]

maybe the cheap method is to wolfram it?

lol