Search over 10,000 free study notes

Find the derivative of f(x)=x³ sin(x).

To do this calculation we need to use the product rule of differentiation: if f(x)=u(x)v(x), then the derivative is f'(x)=u'(x)v(x)+u(x)v'(x). In o...

First of all we are asked to differentiate the function. This can be easily done by multiplying the coefficient of x by its exponent, and then decreasing the exponent by one. Therefore, dy/dx=3x^2+4x We a...

Here you are being asked to differentiate. When differentiating, you times the value of x by its power and then subtract 1 from the power. So for this question you times 6x^(1/2) by 1/2 and then subtract ...

Using cosine rule a.b = |a||b|cos(theta) and the example vectors a = (1,2,3) and b = (3,2,1),First explain why the cosine rule exists, use a geometric proof of the cosine rule. Show the magintude of a=b=r...

To "make y the subject" basically means to get an expression in the form y= a function of the other variables (in this question, x and p). This will involve adding, subtracting, multiplying and ...