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Find the derivative, dy/dx, of y = 8xcos(3x).

Let u= 8x then du/dx = 8Let v= cos(3x) then dv/dx = -3sin(3x)Therefore using the product rule: dy/dx = (cos(3x))(8) + (8x)(-3sin(3x))So dy/dx = 8cos(3x) - 24xsin(3x) .
JC
Answered by Joshua C. • Maths tutor
3992 Views

How do I tell if a curve has a maximum or a minimum?

Firstly we need to find the stationary point on the curve. We know what at a stationary point the gradient is zero so we will find the gradient of the curve. We do this by differentiation, when we have diffe...
CK
Answered by Charlotte K. • Maths tutor
7413 Views

How does integration by parts work ad when to use it?

Integration by parts should be used when you want to integrate a function composed of two factors (we can call them 'u' and 'dv'), where it is fairly easy to derive 'u', while it is difficult or impossible t...
MO
Answered by Michal O. • Maths tutor
3734 Views

A circle with centre C has equation: x^2 + y^2 + 20x - 14 y + 49 = 0. Express the circle in the form (x-a)^2 +(y-b)^2=r^2. Show that the circle touches the y-axis and crosses the x-axis in two distinct points.

Firstly we rearrange the expression to the required form:x 2 + y 2 + 20x - 14y + 49 = 0 which gives (x + 10) 2 - 100 + (y - 7) 2 - 49 + 49 = 0 and so (x - (-10)) 2 + (y -7) 2 = 10 2 Hence a = -10, b = 7 and ...
JI
Answered by John I. • Maths tutor
8017 Views

Integrate ln(x/7) with respect to x

Firstly split up the ln(x/7) = ln(x) - ln(7) using rules of logarithms learnt in your first year of A-levels, as this will reduce any likely error.Secondly, recognise that the -ln(7) term is constant, and so...
AS
Answered by Arjun S. • Maths tutor
3833 Views