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})

\frac{\partial}{\partial x} ((x^{2} + x y)^{3})

2 x y d x + x^{2} d y = 0

x \to 3 + lim (x^{2} + 2 x)

\frac{d y}{d x} = \frac{( 5 y )}{( 2 x + 3 ) ( 3 x + 2 )}

0.125 y^{^{''}} + 4 y^{^{'}} + 20 y = 0

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})