Search our library of Maths A Level questions

Top answers

Maths

A Level

Find dy/dx when y = x(4x + 1)^1/2

Here we can use the product rule where dy/dx = v du/dx + u dv/dx.We let u = x and v = (4x + 1)^1/2 which means we get du/dx = 1 and by using the chain rule we get dv/dx = 1/2(4x + 1)^-1/2

Answered by Rebecca N. • Maths tutor

5294 Views

Express '6cos(2x) +sin(x)' in terms of sin(x).

6cos(2x) +sin(x).Using the double angle formula for cosine (or otherwise), cos(2x) = cos(x)cos(x) - sin(x)sin(x) .cos(2x) = cos^2(x) - sin^2(x) .Hence, 6cos(2x) +sin(x) = 6(cos^2(x) - sin...

Answered by Robbie M. • Maths tutor

4633 Views

Find the x and y coordinates of the turning points of the curve 'y = x^3 - 3x^2 +4'. Identify each turning point as either a maximum or a minimum.

The first part of the problem is solved by differentiating once and equating this to zero:
y = x^3 - 3x^2 +4 .dy/dx = 3x^2 - 6x .dy/dx = x(3x - 6...

Answered by Robbie M. • Maths tutor

11796 Views

Calculate the derivative of the following function: f(x)=cos(3x))^2

The answer can be found by using the chain rule and simple substitution as well as basic knowledge of differentiation.f’(x)= -6cos(3x)sin(3x)

Answered by Jeff M. • Maths tutor

3896 Views

What are the most important trig identities we need to know?

cos^2(A) + sin^2(A) = 1, sin(A+B) = sinAcosB + cosAsinB, cos(A+B) = cosAcosB - sinAsinB, sin2A = 2sinAcosA (if A = B), cos2A = cos^2(A) - sin^2(A) (if A = B), cos2A = 1 - 2sin^2(A) => sin^2(A) = 1/2(1 ...

Answered by Bowen H. • Maths tutor

3590 Views