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How do i use chain rule to calculate the derivative dy/dx of a curve given by 2 "parametric equations": x=(t-1)^3, y=3t-8/t^2

(Explain why it is called "parametric"). The definition of chain rule says that we can re-write the derivative dy/dx in terms of the "parameter t" by dy/dx = (dy/dt) X (dt/dx). (Explain w...
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Answered by Adil F. • Maths tutor
4955 Views

Find the first three terms of the binomial expansion of (3 + 6x)^(1/2).

To find the binomial expansion of this expression we need to use a formula. The formula states that for expressions of (1 + x) n it can be written as: 1 + nx + (n(n-1)x 2 )/2 ... As our initial expression do...
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Answered by Brendan W. • Maths tutor
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Using implicit differentiation, write the expression "3y^2 = 4x^3 + x" in terms of "dy/dx"

To differentiate this expression with respect to "x", any terms comprising of an "x" must multiply their powers with their numerical values and subtract 1 from the power. However to diffe...
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Answered by Brendan W. • Maths tutor
4484 Views

Given a quadratic equation, how do I find the coordinates of the stationary point?

Example curve: y = x 2 + 4x + 5The first step is to differentiate the equation to give us the gradient at a general point. As a quadratic equation is an example of a polynomial, the solution is as follows:dy...
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Answered by Daniel G. • Maths tutor
5768 Views

What is the magnitude and direction of the resultant force of 3N horizontal and 5N vertical?

Magnitude: Find the square root of 3^2+5^2=root of 34=5.83N (3sf) Direction: Draw a triangle with 3N at the bottom, 5N going up and the hypotenuse then represents the resultant force.The direction will be th...
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Answered by Rhiannon H. • Maths tutor
4390 Views