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Differentiate cos(2x)/(x) with respect to x

-cos(2x)/(x 2 ) - 2sin(2x)/(x)
MS
Answered by Marcus S. • Maths tutor
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If z is a complex number, solve the equation (z+i)* = 2iz+1 where the star (*) denotes the complex conjugate.

For questions like these it's easier to first rewrite z as z=x+iy. Once we plug this back into the original equation we get x-iy-i = 2ix-2y+1 Rearranging both sides to group together the real and imaginary t...
AA
Answered by Aysha A. • Maths tutor
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y=4x/(x^2+5)

Find dy/dx Remember quotient rule dy/dx=(u'v-v'u)/v^2 u=4x u'=4 v=x^2+5 v'=2x dy/dx=(20-4x^2)/(x^2+5)^2 (simplified)
JS
Answered by Jeppe S. • Maths tutor
6877 Views

What is the indefinite integral ∫5exp(3-4x)dx ?

∫ 5e 3-4x dx=5∫e 3 e -4x dx=5e 3 ∫e -4x d=5e 3 [(-1/4)e -4x ]=-(5/4)e 3 e -4x =-(5/4)e 3-4x
AM
Answered by Alexandros M. • Maths tutor
6812 Views

Find the 16th term in the following sequence: 3, 5, 7, 9, 11

First find the nth term of the sequence. Start by finding the difference between each term: 3, 5, 7, 9, 11 - the difference between each is 2 therefore it is 2n but this alone gives the sequence: 2, 4, 6, 8....
KS
Answered by Kate S. • Maths tutor
13183 Views