Continuity and Differentiability
Differentiate the following w.r.t. x:cos(logx+ex),x<0
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Find dxdyif x−y=π
The general solution of the DE
If x and y are connected parametrically by the equations given, without eliminating the parameter, Find dxdy.x=a(cost+logtan(2t)),y=asint
Verify Rolle's theorem for the function f(x)=x2+2x−8,x∈[−4,2].
Find the general solution for the following differential equation.xdxdy−y=2x2secx
Using the fact that sin(A+B)=sinAcosB+cosAsinB and the differentiation, obtain the sum formula for cosines.
Find the particular solution of each of the following differential equations when x=2,y=πxdxdy−y+xsinxy=0
Find the general solution of each of the following differential equations:dxdy+(1−cos2x)(1+cos2y)=0.