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})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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))

Compute the slope of

y = 10 x sin (x)

x = a_{0} : 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})

\frac{d}{d x} (9 x (- 2)^{2} - 3 x (- 2) - 1)

\int - 3 tan^{2} (x) d x

\frac{d}{d x} (tan (7 x))

\frac{d}{d x} (2 x^{2} - 8 x + 5)

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})