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Differentiate the following equation: f(x) = 5x^3 + 6x^2 - 12x + 4

Answer:
f'(x) = 15x^2 + 12x -12
This is according to basic rules of differentiation and is a beginner level differentiation question as following:If f(x) = ax^nThen f'(x) = x(nx^n-1)

Answered by Holly K. • Maths tutor

2556 Views

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

Differentiate 5x³ + 4x² + 5x + 9The rules from polynomial differentiation: d(axⁿ) / dx= a(nx^n-1) and df/dx + dg/dx = d (f+g) /dx and dn/dx = 0Using these rules...

Answered by Annabelle S. • Maths tutor

3045 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^1/3y

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. Cons...

Answered by Jordan B. • Maths tutor

2569 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 stude...

Answered by Siam R. • Maths tutor

3134 Views