Top answers

Find the equation of the tangent of the curve y = (8x)/(x-8) at the point (0,0)

We will be using the quotient rule, although the product rule is also usable and can be run through if the student wishes. Firstly, define u = 8x, v = x-8 for simplicity. Then clearly u' = 8, v' = 1, and so ...
TK
Answered by Timofey K. • Maths tutor
3945 Views

Differentiate sin(x^3) with respect to y

For this we must use the chain rule. We start by defining x 3 as a new variable, u = x 3 Can then rewrite the expression as y = sin(u) Chain rule tells us that dy/dx = (dy/du)(du/dx) We can calculate these i...
LB
Answered by Lloyd B. • Maths tutor
7572 Views

The curve has equation y = x^3 - x^2 - 5x + 7 and the straight line has equation y = x + 7. One point of intersection, B, has coordinates (0, 7). Find the other two points of intersection, A and C.

As both equations are equal to y, we can combine them to create a single equation in terms of x: x^3 - x^2 -5X + 7 = x + 7. Shift the equation so the left hand side is equal to 0 on the right: x^3 - x^2 - 6x...
AB
Answered by Alfie B. • Maths tutor
7878 Views

Find the stationary points of the curve y=2*x^3-15*x^2+24*x+17. Determine whether these points are maximum or minimum.

First, differentiate and put the derivative equal to zero. dy/dx=6 x^2-30 x+24=0. Solve this equation to get that x=4 and x=1. Substitute these values into the original equation to get the corresponding valu...
SM
Answered by Shaun M. • Maths tutor
4492 Views

Why is the derivative of x^n, nx^(n-1)?

From the definition of a derivative: f'(x) = lim h->0 ((f(x+h) - f(x)) / h) Let f(x) = x^n --> d\dx x^n = lim h->0 (((x+h)^n - x^n) / h) By binomial expansion, (x+h)^n = x^n + nhx^(n-1) + n(n-1)h^2 ...
JF
Answered by Joshua F. • Maths tutor
5222 Views