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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

6593 Views

5w -3 = 3w + 15

Need to get the numbers on one side, and letters on the other side.

5w = 3w + 15 + 3

5w - 3w = 15 + 3

2w = 18

w = 18/2

w = 9

Answered by Hannah N. • Maths tutor

4400 Views

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

7312 Views

Ian's commute to work is 5km. He needs to be there by 9.00am. He travels at 10 km/h, what time does he need to leave home?

Answer is 8.30am Using the speed = distance/time reference the student would do distance/speed or 5/10 = 0.5 hours

Answered by Isabelle F. • Maths tutor

3256 Views

work out: ( 4 × 10^3 )^2 + 3.5 × 10^7 and give your answer in standard form.

Whenever you have to solve an equation, you must always follow BIDMAS. This means that you should always start with expanding any Brackets, then look at any Indices, then Division, Multiplication, Additio...

Answered by Jade L. • Maths tutor

5986 Views