Continuity and Differentiability
Show that the function f defined by f(x)=∣1−x+x∣, where x is any real number, is a continuous function.
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Differentiate w.r.t. x the function (5x)3cos2x.
Find the second order derivatives of the functions given. x20
Find the second order derivatives of the functions given.e6xcos3x.
Using the fact that sin(A+B)=sinAcosB+cosAsinB and the differentiation, obtain the sum formula for cosines.
Find dxdy, if y=sin−1x+sin−11−x2,−1≤x≤1.
Is it true that x=elogx for all real
Differentiate the following w.r.t x.(i) 3x+2+(2x2+41) (ii) esec2(x)+3cos−1(x) (iii) log7(logx)
Find the second order derivatives of the functions given.logx