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Differentiate y=(3+sin(2x))/(2+cos(2x))

dy/dx = (4cos(2x) + 6sin(2x) + 2)/(2+cos(2x))²

Answered by Matthew B. • Maths tutor

8116 Views

Use the chain rule to show that, if y = sec(x), then dy/dx = sec(x)tan(x).

First, write y in terms of cos(x). We are familiar with cos(x) and know how to differentiate it. We know that sec(x) = 1/cos(x) = (cos(x))^-1. Next, find dy/dx in terms of cos(x) and sin(x). Ag...

Answered by Noah L. • Maths tutor

14426 Views

A right angle triangle has a base of √8 and a height of (√10+3). Show that the area is equal to 2√5+3√2.

The area of a triangle is equal to 1/2 x base x height, so we can write the equation for this question as: Area = 1/2 x √8 x (√10+3) We can then simplify √8 by writing it as its fa...

Answered by Elizabeth H. • Maths tutor

3729 Views

Solve the inequality x^2 > 3(x + 6)

In order to solve this inequality, it is helpful to have all the terms on the left-hand side of the equation. To do this, we can subtract 3(x + 6) from both sides of the equation. This gives us:

x^...

Answered by Joseph M. • Maths tutor

15949 Views