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i) differentiate xcos2x with respect to x ii) integrate xcos2x with respect to x

i) For this question we need to use the product rule as there are two functions that are being multiplied together Product Rule: (uv)'=u'v + v'u Apply this formula to the problem: xcos2x => u=x, u'=1 =&gt...
CP
Answered by Carina P. • Maths tutor
7092 Views

Find the cube roots of i in the form a+bi, where a, b are real numbers.

Write i in terms of an exponential, so i = e^(i pi/2).Then the three roots of i are:z_1 = [e^(i pi/2)]^(1/3) = e^(i pi/6) = sqrt(3)/2 + i/2z_2 = e^[i (pi/6 + 2pi/3)] = e^(i 5pi/6) = -sqrt(3)/2 + i/2z_3 = e^[...
JC
Answered by Joanna C. • Maths tutor
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How do we know the derivative of x^n

What does derivative mean? The derivative of a function the represents the gradient of the function for each value of x. Remark that the gradient of a function at point (x,f(x)) is equal to the gradient of a...
TP
Answered by Thomas P. • Maths tutor
3917 Views

Solve x^2 + 5x – 24 = 0

Being a quadratic equation in the following form,the simplest way to solve would be through the quadratic formula which goes as follows: The first step to solving is therefore to identify a, b, c, within our...
MK
Answered by Mohammed K. • Maths tutor
5870 Views

If f(x)=7xe^x, find f'(x)

f(x) = 7xe x Using the product rule: [f'(x)=u*(dv/dx)+ v*(du/dx)]Let u=7x and v=e x Therefore, du/dx=7 and dv/dx=e x Hence, f'(x) = 7xe x + 7e x
LM
Answered by Lanya M. • Maths tutor
4972 Views