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How would you derive y = function of x; for example: y = 3x^3 + x^2 + x

The best way to remember derivatives is to use algebra, and the general function is y = axⁿ -> dy/dx = anx^n-1

So for this equation dy/dx = (3x3)x^3-1 + (2x1)x

Answered by George A. • Maths tutor

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Find the gradient of the curve y = x^2(ln(x)) at x = e

We'll need to use the product rule.

Let's take u = x^2 -> du/dx = 2x, and v = ln(x) -> dv/dx = 1/x

Then dy/dx = x^2(1/x) + 2xln(x) = x + 2xln(x)

Substituting our x value gives (...

Answered by Charlie R. • Maths tutor

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AQA PC4 2015 Q5 // A) Find the gradient at P. B) Find the equation of the normal to the curve at P C)The normal P intersects at the curve again at the point Q(cos2q, sin q) Hence find the x-coordinate of Q.

A) We need to find dy/dx. We know that dy/dx =(dy/dt)/(dx/dt). Differentiating each parametric equation we get: dx/dt= -2sin(2t) {using the chain rule and knowing that cos differentiates to -sin.} dy/dt= ...

Answered by Tutor68191 D. • Maths tutor

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Find the gradient of the line with equation 2x + 5y = 7

-2/5

Answered by Alison M. • Maths tutor

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Given the intensity of A-Level studies, what is the best way one can go about ensuring all tasks are completed in time?

The best way to solve any complex problem is to start off by formulating a general overview of the problem. This is useful as it allows you to see the overall 'big' picture and allows you to really compre...

Answered by Bahir Z. • Maths tutor

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