What is the tangent of y=x+sin(x) ?

The tangent of y=x+sin(x) is y=(1+cos(a_{0}))x-a_{0}cos(a_{0})+sin(a_{0})

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tangent of y=x+sin(x)

tangent of

y = x + sin (x)

y = (1 + cos (a_{0})) x - a_{0} cos (a_{0}) + sin (a_{0})

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} + sin (a_{0}))

Find the slope of

y = x + sin (x) : \frac{d y}{d x} = 1 + cos (x)

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = 1 + cos (a_{0})

Find the line with slope m=

1 + cos (a_{0})

and passing through

(a_{0}, a_{0} + sin (a_{0})) : y = (1 + cos (a_{0})) x - a_{0} cos (a_{0}) + sin (a_{0})

y = (1 + cos (a_{0})) x - a_{0} cos (a_{0}) + sin (a_{0})

\frac{d}{d x} ((2 x^{3} - 12 x)^{\frac{4}{3}})

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 4 y ^{2}})

\int \frac{1}{( x ^{2} - x )} d x

\frac{\partial}{\partial x} (y cos (x - y))

64 y^{^{''}} + 80 y^{^{'}} + 25 y = 0, y (0) = a, y^{^{'}} (0) = - 5

What is the tangent of y=x+sin(x) ?
The tangent of y=x+sin(x) is y=(1+cos(a_{0}))x-a_{0}cos(a_{0})+sin(a_{0})