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Find the slope of the tangent to the cur...

Find the slope of the tangent to the curve
y=(1+x)sin x at `x=pi/4`

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Given curve is y=(1+x)sinx
`therefore dy/dx=(1+x)cosx+sinx
`therefore`Required slope of the tangent to the given curve at `x=pi/4` is
`[dy/dx]_(x=pi/4)= (1+pi/4)"cos"pi/4+"sin"pi/4=1/sqrt2(2+pi/4)`
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