Top answers

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 necessar...
BJ
Answered by Bevan J. • Maths tutor
4071 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 +1) = ( (-27x^3 -63x^2...
SB
Answered by Samuel B. • Maths tutor
4223 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) Stationary points occur w...
RB
Answered by Russell B. • Maths tutor
5635 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/y dy = ...
ST
Answered by Sam T. • Maths tutor
7982 Views

Differentiate y = lnx + 4x^2 + 3e^4x with respect to x

lnx differentiates to 1/x 4x^2 differentiates to 8x 3e^4x differentiates to 12e^4x therefore the answer is: 1/x + 8x + 12e^4x
DS
Answered by Dhylon S. • Maths tutor
4506 Views