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Given y = ln((2x+3)/(7x^3 +1)). Find dy/dx

 y = ln(2x+3 / 7x^3 +1)

d/dx(2x+3 / 7x^3 + 1) by quotient rule which is(v.du/dx - u.dv/dx) / v^2  where u=2x+3 and v=7x^3 +1   gives (-27x^3 -63x^2 +2) / (7x^3 +1)^2

so d/dx(ln(2x+3 / 7x^3 +...

SB
Answered by Samuel B. Maths tutor
3967 Views

Given the function y=(x+1)(x-2)^2 find i) dy/dx ii) Stationary points and determine their nature

Here we have a function made from the product of two functions, so we canuse the product differenciation rule.

y=uv  =>  dy/dx=udv/dx + vdu/dx

Therefore dy/dy=(x-2)^2 + 2(x-2)(x+1)

RB
Answered by Russell B. Maths tutor
5227 Views

Solve algebraically: 6a+b = 16 and 5a - 2b = 19

6a + b = 16 (1)

5a - 2b = 19 (2)

(1) x 2: 12a + 2b =32

(1) + (2): 12a + 2b + 5a - 2b = 32 + 19 = 51

17a = 51

a = 51 / 17 = 3

Substitue a = 3 back into (1): (6 x 3...

NR
Answered by Niva R. Maths tutor
3303 Views

Find the general solution to the differential equation '' (x^2 + 3x - 1) dy/dx = (2x + 3)y ''

Now although this might seem like quite a complex question at first, it's a little less intimidating when we take a while to look at it- you might notice that we can seperate x and y terms like so:
1...

ST
Answered by Sam T. Maths tutor
7687 Views

Solve 0=X^2 +5x +4

0= (x + 4)(x + 1)

x= - 4

x= - 1

RW
Answered by Rebecca W. Maths tutor
3015 Views

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