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Find the derivative of the following function. Derivative rules and possible algebra rewriting are required.
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- Find the first derivative of y = (x – 1) √ (2x – x2) + arcsin (x – 1), and y = arctan [ (3 sin x) / (4 + 5 cos x) ], and y = ( ex – e –x ) / (ex + e –x ) Simplify the answer but make the solution detailed and clear.What is q'(x) when q(x)=ln((5x^2+x+7)/((x^2/3)(sin(x)))What is the derivative of the: y = (1 + cos2 x sin x2)3/2
- Differentiate the function. y= ln(x3 sin2 x)(a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this equation to obtain f' (x) + g' (x) = 0. This implies f'(x) = -g'(x). (b) f' (x) = 2 sin x cos x, and g'(x) = 2(cosx)(-sinx) = -2sin x cos x. So, f'(x) = -g'(x).