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If x^2 + 4x + 3xy + y^3 = 6, find the first derivative.

This is an example of implicit differentiation. We differentiate with respect to x, remembering that y is a function of x. The terms without a 'y' differentiate as normal by the power rule nx^n-1

Answered by Olateju O. • Maths tutor

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Rob has a bag with white, black and blue counters. There are twice as many blue counters than there are white. A qaurter of all the counters are black. If there are 5 white counters, how many counters are in the bag.

White:blue is 1:2. (There are twice as many blue counters)if there are 5 white counters there are 10 blue counterswhite + blue = 15in the bag there are the 15 white and blue counters PLUS the blacki.e. In...

Answered by Aurimas K. • Maths tutor

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In a right-angled triangle calculate the length of the hypotenuse when the side lengths at 5cm and 7cm. Leave your answer as a surd.

Using pythagoras’ theorem:a^2 + b^2 = c^2
hypotenuse = sqrt(5^2 + 7^2) = sqrt(25+49) = sqrt(74)

Answered by • Maths tutor

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Solve the equation x^2 + 10x + 24 = 0

So, we are dealing here with a quadratic equation as it is written in the form ax^2 + bx +c = 0 To tackle this we will firstly need to factorise the equation, we need to find two numbers that will multipl...

Answered by Aleema S. • Maths tutor

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A curve C with an equation y = sin(x)/e^(2x) , 0<x<pi has a stationary point at P. Find the coordinates ofP?

Firstly notice that to find a stationary point of a curve with an equation, the best first step is often to differentiate the expression. Then solve the equation for x when dy/dx = 0. In this case the y e...

Answered by Rufus E. • Maths tutor

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