What is the tangent of y=10xsin(x) ?

The tangent of y=10xsin(x) is y=10(sin(a_{0})+a_{0}cos(a_{0}))x-10a_{0}^2cos(a_{0})

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tangent of y=10xsin(x)

tangent of

y = 10 x sin (x)

y = 10 (sin (a_{0}) + a_{0} cos (a_{0})) x - 10 a_{0}^{2} cos (a_{0})

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 10 a_{0} sin (a_{0}))

Find the slope of

y = 10 x sin (x) : \frac{d y}{d x} = 10 (sin (x) + x 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 = 10 (sin (a_{0}) + a_{0} cos (a_{0}))

Find the line with slope m=

10 (sin (a_{0}) + a_{0} cos (a_{0}))

and passing through

(a_{0}, 10 a_{0} sin (a_{0})) : y = 10 (sin (a_{0}) + a_{0} cos (a_{0})) x - 10 a_{0}^{2} cos (a_{0})

y = 10 (sin (a_{0}) + a_{0} cos (a_{0})) x - 10 a_{0}^{2} cos (a_{0})

What is the tangent of y=10xsin(x) ?
The tangent of y=10xsin(x) is y=10(sin(a_{0})+a_{0}cos(a_{0}))x-10a_{0}^2cos(a_{0})