Practice problem
Find the derivative of f(x)f(x)f(x). f(x)=1+cosxx+sinxf(x)=\frac{1+\cos x}{x+\sin x}f(x)=x+sinx1+cosx
f′(x)=−sinx1+cosxf'(x)=-\frac{\sin x}{1+\cos x}f′(x)=−1+cosxsinx
f′(x)=(1+cosx)2(x+sinx)2−sinxx+sinxf'(x)=\frac{(1+\cos x)^2}{(x+\sin x)^2}-\frac{\sin x}{x+\sin x}f′(x)=(x+sinx)2(1+cosx)2−x+sinxsinx
f′(x)=1x−tan2xf'(x)=\frac1x-\tan^2 xf′(x)=x1−tan2x
f′(x)=−xsinx+2cosx+2(x+sinx)2f'(x)=-\frac{x\sin x+2\cos x+2}{(x+\sin x)^2}f′(x)=−(x+sinx)2xsinx+2cosx+2
Type a concept, like “slope” or “photosynthesis”.
