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How do you integrate x* (exp(x))??

The easiest method to use in this incidence is integratation by parts.

So let u=x and dv/dx=exp(x). Therefore du/dx=1 and v=exp(x).

Then we use the formula where integral(udu/dx)=uv...

Answered by Harmony J. • Maths tutor

9156 Views

Differentiate y=x^3*(x^2+1)

As this is a product of two functions it is necessary to use the product rule for differentiation. Therefore one of the functions must labeled v and the other u. i.e. u=x^3 and v=(x^2+1). It is then neces...

Answered by Bevan J. • Maths tutor

3197 Views

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 +...

Answered by Samuel B. • Maths tutor

3556 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)

Answered by Russell B. • Maths tutor

4470 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...

Answered by Sam T. • Maths tutor

7112 Views