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How do you solve the following simultaneous equations? Equation 1: 2x + 3y = 13 Equation 2: 3x - y = 3

There are various ways to solve simultaneous equations. The two easiest are by elimiation and by substitution. By Elimation When solving by elimination you want to ensure that you only have one variable (x o...
LS
Answered by Luke S. • Maths tutor
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What actually are sin, cos and tan?

This is a common question asked by my students when they first learn about trigonometry. First draw a unit circle on the plane and the graphs of sine and cosine next to it. The circle obviously has 360 degre...
LP
Answered by Leon P. • Maths tutor
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The point P (4, –1) lies on the curve C with equation y = f( x ), x > 0, and f '(x) =x/2 - 6/√x + 3. Find the equation of the tangent to C at the point P , giving your answer in the form y = mx + c. Find f(x)

First step is to understand all the notation, i.e. the prime for derivative. We then need to understand that the derivative is the gradient of the tangent at a point. In this case at the point P we can find ...
LP
Answered by Leon P. • Maths tutor
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Let g (x) = 2x sin x . (a) Find g′(x) . (b) Find the gradient of the graph of g at x = π .

a) f'(x)=uv'+vu' if f(x)= uv u=2x u'=2 v=sin(x) v'=cos(x) g'(x)=2x cos(x) +2sin(x) b) g'(π) = 2π cos(π)+2sin(π) = 2 π (-1) + 2 (0) g'(π) = -2π
MB
Answered by Matias B. • Maths tutor
10773 Views

Differentiate sin(x)cos(x) using the product rule.

The product rule states (assuming x' is the differential of x): (fg)​′​​=f​′​​g+fg​′​​ Substitute the values into the rule: (sin(x)cos(x))' = sin(x)'cos(x) + sin(x)cos(x)' (sin(x)cos(x))' = cos 2 (x) - sin 2...
MP
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