Find the indicated derivative dx dz dx Need Help? Read it Show My Work (optional

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Find the indicated derivative dx dz dx Need Help? Read it Show My Work (optional) +-1 points HarMatnAp11 9.5.020 Find the indicated derlvative (x + 2)(x-3) f'(x) for fix)- f(x) - Need Help? Read ItWatch D Show My Work (optional + -/1 points HarMathAp11 9.5.023 Write the equation of the tangent line to the graph of y = (10x2-6x + 1)(1 + 2x) at x-1, check the reasonableness of your answer by graphing both the function and the tangent line. Need Help? Read it Show My Work (optional +:2 points HarMathA01 19.5.041 MI Suppose the revenue (in dollars) from the sale of x units of a product is given by R(x) = 62x-68x 2x 2 Find the marginal revenue when 67 units are sold. (Round your answer to the nearest dollar.) Interpret your result. When 67 units are sold, the projected revenue from the sale of unit 68 would be $ Need Help? Read It Master It

Explanation / Answer

z = x4 + [ x2 / (1-x-2x2) ] ; We know that d/ dx (xn) = n * xn-1

dz/dx = 4x3 + [ (1-x-2x2) 2x - x2 (-1-4x) ]/ (1-x-2x2) 2
=4x3 + ( 2x-2x2 -4x3 +x2+4x3 ) / (1-x-2x2) 2
= [4x3 ]   + [ - x2 +2x ] / (1-x-2x2)2

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f(x) = (x+2) (x-3) / (x2 +6) = (x2 +2x - 3x -6 )/ (x2+6) = (x2 -x -6) / (x2 +6)
f'(x) = d(f(x) ) / dx = [(x2 +6) ( 2x-1) - (x2-x-6)(2x) ] / (x2+6) 2
= [ 2x3 -x2 +12x -6 - 2x3 +2x2 + 12x ] / (x2 +6)2
= (x2 +24x -6) / (x2 +6) 2

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