Find the derivative of f(x)=xsinxf(x) = x \sin xf(x)=xsinx.
Use Product Rule with u=xu = xu=x and v=sinxv = \sin xv=sinx. f′(x)=u′v+uv′f'(x) = u'v + uv'f′(x)=u′v+uv′ =(ddxx)(sinx)+(x)(ddxsinx)= (\frac{d}{dx} x)(\sin x) + (x)(\frac{d}{dx} \sin x)=(dxdx)(sinx)+(x)(dxdsinx) =(1)(sinx)+(x)(cosx)= (1)(\sin x) + (x)(\cos x)=(1)(sinx)+(x)(cosx) =sinx+xcosx= \sin x + x \cos x=sinx+xcosx
Compute the derivative of f(x)=x+sinxx+cosxf(x) = \frac{x + \sin x}{x + \cos x}f(x)=x+cosxx+sinx.
Analyze lines and planes in three-dimensional space.