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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 +1) = ( (-27x^3 -63x^2...
SB
Answered by Samuel B. • Maths tutor
4307 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...
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Answered by Russell B. • Maths tutor
5727 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 = ...
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Answered by Sam T. • Maths tutor
8059 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
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Answered by Dhylon S. • Maths tutor
4590 Views

Consider the functions f and g where f (x) = 3x − 5 and g (x) = x − 2 . (a) Find the inverse function, f^−1 . (b) Given that g^−1(x) = x + 2 , find (g^−1 o f )(x) . (c) Given also that (f^−1 o g)(x) = (x + 3)/3 , solve (f^−1 o g)(x) = (g^−1 o f)(x)

(a) Start with f(x)= 3x − 5; y=3x - 5, and switch x and y before rearanging to get y in terms of x again: y=3x - 5 x=3y - 5 (x+5)/3=y Therefore f^−1(x)=(x+5)/3 (b) Start with f(x)= 3x − 5 and and sub result ...
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Answered by Isobel B. • Maths tutor
20259 Views