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Differentiate 5x^3 + 4x^2 + 5x + 9

Differentiate 5x 3 + 4x 2 + 5x + 9The rules from polynomial differentiation: d(ax n ) / dx= a(nx n-1 ) and df/dx + dg/dx = d (f+g) /dx and dn/dx = 0Using these rules in conjunction we get : 5(3x 3-1 ) + 4(2x...
AS
Answered by Annabelle S. • Maths tutor
4076 Views

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
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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
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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

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
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