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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
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A right-angled triangle has an angle of 30 degrees and its hypotenuse has a length of 9cm. Find the length of either of the triangle's other two sides.

Please note that this solution is easier to explain with 2 diagrams The side opposite of the 30 degree angle: If we have the hypotenuse and require the length of the opposite side then we would use sin ( Soh...
CB
Answered by Ciaran B. • Maths tutor
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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
4327 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
5755 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) + b = 16 18 + b = 16 b = 16 - 18 = - 2 Subs...
NR
Answered by Niva R. • Maths tutor
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