Question

find an equation of the tangent line to teh curve y=(xsin(x))/(1+x) at the point (0,0).

Answer 1

tangent line:
\[y - y_1 = \frac{dy}{dx}(x-x_1)\]
(x1,y1) = (0,0)
so
\[y = \frac{dy}{dx} x\]

Answer 2

to find derivative use product and quotient rules

Answer 3

f = x*sin(x)
f' = sin(x) + xcos(x)

g = 1+x
g' = 1

\[(\frac{f}{g})' = \frac{f'g - fg'}{g^{2}}\]

Answer 4

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