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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
7395 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
3555 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
6875 Views

When using the trapezium rule to approximate area underneath a curve between 2 limits, what is the effect of increasing the number of strips used?

Ideally to find the exact area under the curve, we would integrate the function and substitute in the bounds given. However, using the trapezium rule gives an approximation whereby using more trapezia increa...
MM
Answered by Manan M. • Maths tutor
10327 Views