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A radio sells for £63, after a 40% increase in the cost price. Find the cost price.

X+2/5X = 63 or 63 = 140% First we need to understand that the original price (X) has been increased by 40%. Hence, by 2/5 (40/100 = 40%) of its original value, in other words, 2/5X. To find the answer we the...
GB
Answered by Gianluca B. • Maths tutor
6639 Views

Given that y=(4x+1)^3sin 2x , find dy/dx .

So this function is the product of two functions of x, so we use the product rule to differentiate it. The rule states if y=uv, dy/dx=(du/dx)v+(dv/dx)u. In this function we assign u=(4x+1) 3 and v=sin2x. Whe...
TF
Answered by Tom F. • Maths tutor
7298 Views

Solve the ODE y' = -x/y.

we have dy/dx = -x/y , so we treat the differentials as fractions and write y dy = -x dx. Now integrating the left side with respect to y and the right side with respect to x, we have y 2 /2 = -x 2 /2 + C. W...
JM
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I've been told that I can't, in general, differentiate functions involving absolute values (e.g. f(x) = |x|). Why is that?

When you differentiate a function which has only one parameter, like f(x), you are finding a new function, f'(x), which gives the gradient of your original function at every point. You'll probably remember t...
RW
Answered by Richard W. • Maths tutor
3474 Views

What are the solutions of (x^3)+6 = 2(x^2)+5x given x = 3 is a solution?

Firstly we will put this into a form equal to zero, by rearranging to get x 3 -2x 2 -5x+6 = 0. This is because in order to solve a polynomial we first need to set it equal to zero. We now know that the value...
WB
Answered by William B. • Maths tutor
6798 Views