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2cot2x= 2(1/tan2x)= 2(1/(2tanx/1-tan²x))=2(1-tan²x)/2tanx= (1-tan²x)/tanx(1-tan²x)/tanx +tanx=(1-tan²x)/tanx +tan²x/tanx=1/tanx=cotx

f^-1(x)=(e^x-1)/3 g(x)=3/(3x+1)

The product rule is used to differentiate this since we are trying to differentiate the product of 2 parts--x and ln(x)So using the product rule which is d/dx=u.(dv/dx) +v.(du/dx)let u=x and v=ln(x)then d...

Start with finding limits by setting 3x - x^2 = 0, then factorise x(3 - x) = 0. Therefore x = 0 or 3. The area is the integral of 3x - x^2 between x = 0 and 3, sub in 3 and 0 into 3(x^2)/2 - (x^3)/3, whic...

2x/[(x+1)(2x-4)] = [A/(x+1) + B/(2x-4)]x = A(x-2) + B(x+1)x = -1-1 = A(-3)A = 1/3x = 2 2 = B(3)B = 2/3 therefore.... 2x/[(x+1)(2x-4)] ...