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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
3914 Views

How do you make f the subject of the following a = c/d + e/f

1)Multiply out the right hand side to give a common denominator: a= (Cf+de)/df2) Cross multiply to get rid of the denominator fda = cf + de3) bring all terms containing f to the same side and factorise fda -...
KD
Answered by Kwaku D. • Maths tutor
3547 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
3469 Views

How do i find 30% of 70?

To begin with we need to understand what a percentage is. It is simply a proportional that shows a number as parts of a hundred. So 30% is the same as saying 30/100 which can be simplified by dividing the nu...
KR
Answered by Kevin R. • Maths tutor
178356 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
4066 Views