What is the tangent of 5x+4cos(x) ?

The tangent of 5x+4cos(x) is y=(5-4sin(a_{0}))x+4a_{0}sin(a_{0})+4cos(a_{0})

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tangent of 5x+4cos(x)

tangent of

5 x + 4 cos (x)

y = (5 - 4 sin (a_{0})) x + 4 a_{0} sin (a_{0}) + 4 cos (a_{0})

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 5 a_{0} + 4 cos (a_{0}))

Find the slope of

y = 5 x + 4 cos (x) : \frac{d y}{d x} = 5 - 4 sin (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 = 5 - 4 sin (a_{0})

Find the line with slope m=

5 - 4 sin (a_{0})

and passing through

(a_{0}, 5 a_{0} + 4 cos (a_{0})) : y = (5 - 4 sin (a_{0})) x + 4 a_{0} sin (a_{0}) + 4 cos (a_{0})

y = (5 - 4 sin (a_{0})) x + 4 a_{0} sin (a_{0}) + 4 cos (a_{0})

What is the tangent of 5x+4cos(x) ?
The tangent of 5x+4cos(x) is y=(5-4sin(a_{0}))x+4a_{0}sin(a_{0})+4cos(a_{0})