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A curve has equation 3x^4/3-16y^3/4=32. By differentiating implicitly find dy/dx in terms of x and y. Hence find the gradient of the curve at the point (8,1).

3x 4/3 -16y 3/4 =32Differentiating implicitly:4x 1/3 -12y -1/4 (dy/dx)=0Simplifying and rearranging:x 1/3 =3y -1/4 (dy/dx)dy/dx=1/3(x 1/3 y 1/4 ) Finding dy/dx using the (x,y) co-ordinates given:dy/dx=1/3(8 ...
BG
Answered by Ben G. • Maths tutor
3983 Views

Show the sum from n=0 to 200 of x^n given that x is not 1, is (1-x^201)/(1-x) hence find the sum of 1+2(1/2)+3(1/2)^2+...+200(1/2)^199

Let the first term of a geometric progression be 'A', define the geometric sum, which we will call 'S', of 'Ax^n' for each integer n to be the sum from n=0 to r of 'Ax^n'. Hence S=A+Ax+Ax^2+...+Ax^r. Conside...
JB
Answered by Jordan B. • Maths tutor
3527 Views

How to integrate lnX?

Firstly I would ask the student what different ways of integration do we know so far? After eliminating each possibility, such as the answer is not XlnX, as this differentiates via product rule, the student ...
SR
Answered by Siam R. • Maths tutor
4133 Views

How to differentiate y=2x(x-2)^5 to find dy/dx?

Firstly, you should formulate the problem by using the product rule, which is: dy/dx = u'v + v'u By assigning u=2x and v=(x-2) 5 , the terms u' and v' can be obtained knowing that u' simply means differentia...
AP
Answered by Anup P. • Maths tutor
6306 Views

If h(x) = 2xsin(2x), find h'(x).

Differentiate using product rule as expression consist of two functions.Product Rule: d(f(x)g(x))/dx = g(x).f'(x) + f(x).g'(x)Chain Rule: d(f(g(x)))/dx = g'(x) . f'(g(x)) Let: f(x) = 2x f'(x) = 2 - simple di...
MS
Answered by Meer S. • Maths tutor
4310 Views