First using the double angle formula;
2sinAcosA = sin(2A)
Therefore d/dA (sin2A) = cos(2A) * 2 = 2cos(2A)
We multiply by the two due to the chain rule, where we must multiply by the derivative of the angle.
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dy/dx = 3 integral = (3x^2)/2
y = Sin(x) dy/dx = Cos(x)
log 3 is a constant, so d/dx log3, like d/dx of any constant, equals zero.
The open channel flow has a free surface whereas the pipe flow has a closed surface.
The derivative of the ln function is the function 1/x. So the derivative of ln1.01 should be 1/1.01 = 0.990099... ------------------------- Well I may be looking at this slightly different, but the question as stated "differentiate ln(1.01)" would be 0 seeing as ln(1.01) is itself a constant (irrational) number. The derivative of any constant is zero. If the intended question was ln(x)d/dx where x=1.01 then I agree with the above answer.