Testbsk: Student Solutions Manual – Calculus: Early Transcendentals, 9th Edition (2021) by James Stewart | Full Step-by-Step Solutions

Student Solutions Manual – Calculus: Early
Transcendentals, 9th Edition (2021) by
James Stewart

Product Rule - answer-d/dx [ u(x) v(x)] = u'(x) v(x) + u(x) v'(x)



Quotient Rule - answer-d/dx [u/v] = (vu'-uv')/v²



Derivatives of Trig Functions - answer-d/ dx [sinx] = cosx



d/dx [ cosx] = -sinx



d/dx [ tanx] = sec^2 x



d/dx [cot] = -csc^2 x



d/dx [ sec x] = secxtanx



d/dx [ cscx] = -cscxcotx



the chain rule - answer-d/dx [f(g(x))] = f'(g(x)) g'(x)



derivative of an exponential function - answer-d/dx [b^x] = b^x lnb


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, Implicit Differentiation - answer-The process of finding the derivative of a dependent variable in
an implicit function by differentiating each term separately, by expressing the derivative of the
dependent variable as a symbol, and by solving the resulting expression for the symbol.



Inverse Trig Derivatives - answer-d/dx [arcsinx]= 1/√1-x^2



d/dx [arccosx] = -1/ √1-x^2



d/dx [arctanx]= 1/1+x^2



d/dx [arccotx] = -1/1+x^2



d/dx [ arcsecx] = 1/ x√x^2-1



d/dx [arccscx] = -1/ x√x^2-1



log derivatives - answer-d/dx [ logbX] = 1/xlnb



d/dx [lnx] = 1/x



Rates of change in physics - answer-t= time (sec)



s(t)= position (ft or m)




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