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Find dy/dx of the equation (x^3)*(y)+7x = y^3 + (2x)^2 +1 at point (1,1)

Use the product rule d(u.v)/dx = u.(dv/dx) + v(du/dx). Calculate the LHS as such first. (Demonstrate on whiteboard.) Then calculate the RHS. (Demonstrate on whiteboard.) Group the dy/dx terms on one side ...

Answered by Sophie P. • Maths tutor

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The curve C is defined by x^3 – (4x^2 )y = 2y^3 – 3x – 2. Find the value of dy/dx at the point (3, 1).

When we find dy/dx we find the gradient of the curve at (3,1). Start by differentiating the left hand side (LHS) like so.. (whiteboard). Remember every time we differentiate a y value we multiply by dy/dx...

Answered by Caitlin R. • Maths tutor

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Simplify the following expression to a fraction in its simplest form: [(4x^2 + 6x)/(2x^2 - x -6)] - [(12)/(x^2 - x - 2)]

2(x+3)/(x+1)

Answered by Dylan H. • Maths tutor

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Express (3+ i)(1 + 2i) as a complex number in the form a+bi where a and b are real numbers.

One can treat complex multiplication as polynomial multiplication, but remembering i^2 = -1. To perform polynomial multiplication, multiply each term one by one, then add them together. Hence (3+i)(1+2i) ...

Answered by Alvin S. • Maths tutor

9115 Views

(Using the Quotient Rule) -> Show that the derivative of (cosx)/(sinx) is (-1)/(sinx).

This question is a typical example aimed to test the student's understanding of the quotient rule, a technique which is used very often in calculus problems. Answer: For a function f(x) = cosx/sinx = u/v,...

Answered by Mark H. • Maths tutor

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