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y = (2x -3)^3

y = (2x)^3 + 3.((2x)^2)(-3) + 3.(2x).(-3)^2 + (-3)^2 using Pascal's Triangle.

y = 8x^3 - 36x^2 + 54x - 27 

dy/dx = 24x^2 - 72x + 54

at point (1,-1); dy/dx = 24 -7...

There is an initial subtle difficulty to this question, and it highlights understanding of the relationship between natural logarithms and the exponential function. One of the ways to solve this question,...

Try y=Ae^bx diffrentiate this (dy/dx = Abe^bx) and sub into 2dy/dx -5y = 0 to find complementary function. 2Abe^bx - 5Ae^bx = 0 2b - 5 = 0 b = 2.5 Find the particul...

This can't be integrated directly as y appears in the numerator and denominator. This is an indication that you must integrate by parts. A/y + B/(3y+2) = (3y - 4)/y(3y + 2) A and B must be found. Multiply...

z-2+3i times z-2-3i = z²-4z+13. z³-2z²+5z+26 divided by z²-4z+13 = z+2. Therefore the real root is z=-2.