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f(x) = x^3 + 3x^2 + 5. Find f'(x) and f''(x).

With differentitaion you multiply the fatcor it's raised by and minus one from the order e.g. y = x^n so y' = nx^(n-1) So f'(x) = 3x^2 + 6x and f''(x) = 6x + 6
NS
Answered by Nikita S. • Maths tutor
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Solve the equation (2x + 3 / x - 4) - (2x - 8 / 2x + 1) = 1

Solve the equation (2x + 3 / x - 4) - (2x - 8 / 2x + 1) = 1 Answer To start off, we must find the common denominator between the two fractions. When dealing with complex problems, which include letters and n...
JB
Answered by Jonathan B. • Maths tutor
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What is the equation of the tangent to the circle (x-5)^2+(y-3)^2=9 at the points of intersection of the circle with the line 2x-y-1=0

Teh points of intersection can be found by subbing in y=2x-1 to the equation of the circle. (x-5) 2 +(2x-1-3) 2 =5x 2 -26x+33=9 so we have 5x 2 -26x+24=0. Solving the quadratic equation gives x 1 =4 and x 2 ...
TD
Answered by Tutor67416 D. • Maths tutor
3995 Views

When do I use the product rule as opposed to the chain rule?

The product rule is used when two functions of x are multiplied by each other, hence, product. So this can be used to differnetiatate 3x 2 * x+1 or more complex functions like sinxcosx. The chain rule is use...
LU
Answered by Lota U. • Maths tutor
4593 Views

Let f (x) = sin(x-1) , 0 ≤ x ≤ 2 π + 1 , Find the volume of the solid formed when the region bounded by y =ƒ( x) , and the lines x = 0 , y = 0 and y = 1 is rotated by 2π about the y-axis.

Draw a rough sketch of the graph of f(x) = sin(x-1) to get an idea of what the region looks like. Realise that the normal volume of revolution for the area between x axis and the f(x) is given by V = pi* int...
AS
Answered by Ankur S. • Maths tutor
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