What is the tangent of f(x)=(x+2sin(x)) ?

The tangent of f(x)=(x+2sin(x)) is y=(1+2cos(a_{0}))x-2a_{0}cos(a_{0})+2sin(a_{0})

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tangent of f(x)=(x+2sin(x))

tangent of

f (x) = (x + 2 sin (x))

y = (1 + 2 cos (a_{0})) x - 2 a_{0} cos (a_{0}) + 2 sin (a_{0})

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} + 2 sin (a_{0}))

Find the slope of

f (x) = (x + 2 sin (x)) : \frac{df ( x )}{d x} = 1 + 2 cos (x)

Compute the slope of

f (x) = (x + 2 sin (x))

x = a_{0} : m = 1 + 2 cos (a_{0})

Find the line with slope m=

1 + 2 cos (a_{0})

and passing through

(a_{0}, a_{0} + 2 sin (a_{0})) : y = (1 + 2 cos (a_{0})) x - 2 a_{0} cos (a_{0}) + 2 sin (a_{0})

y = (1 + 2 cos (a_{0})) x - 2 a_{0} cos (a_{0}) + 2 sin (a_{0})

\int \frac{x - 3}{3 - 4 x ^{2}} d x

(4 X - 1)^{2} (3 X - 1)^{- 2}

\frac{d y}{d x} = 8 x y

\int \frac{x}{196 x ^{2} - 1} d x

\int \frac{x + 1}{( x ^{2} + 2 x - 3 ) ^{2}} d x

What is the tangent of f(x)=(x+2sin(x)) ?
The tangent of f(x)=(x+2sin(x)) is y=(1+2cos(a_{0}))x-2a_{0}cos(a_{0})+2sin(a_{0})