What is the tangent of (12)/((2sin(x)+6cos(x))^2) ?

The tangent of (12)/((2sin(x)+6cos(x))^2) is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tangent of (12)/((2sin(x)+6cos(x))^2)

tangent of

\frac{12}{( 2 sin ( x ) + 6 cos ( x ) ) ^{2}}

y = - \frac{24 ( 2 cos ( a _{0} ) - 6 sin ( a _{0} ) )}{( 2 sin ( a _{0} ) + 6 cos ( a _{0} ) ) ^{3}} x + \frac{12}{( 2 sin ( a _{0} ) + 6 cos ( a _{0} ) ) ^{2}} + \frac{24 a _{0} ( 2 cos ( a _{0} ) - 6 sin ( a _{0} ) )}{( 2 sin ( a _{0} ) + 6 cos ( a _{0} ) ) ^{3}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{12}{( 2 sin ( a _{0} ) + 6 cos ( a _{0} ) ) ^{2}})

Find the slope of

y = \frac{12}{( 2 sin ( x ) + 6 cos ( x ) ) ^{2}} : \frac{d y}{d x} = - \frac{24 ( 2 cos ( x ) - 6 sin ( x ) )}{( 2 sin ( x ) + 6 cos ( x ) ) ^{3}}

Compute the slope of

y = \frac{12}{( 2 sin ( x ) + 6 cos ( x ) ) ^{2}}

x = a_{0} : m = - \frac{24 ( 2 cos ( a _{0} ) - 6 sin ( a _{0} ) )}{( 2 sin ( a _{0} ) + 6 cos ( a _{0} ) ) ^{3}}

Find the line with slope m=

- \frac{24 ( 2 cos ( a _{0} ) - 6 sin ( a _{0} ) )}{( 2 sin ( a _{0} ) + 6 cos ( a _{0} ) ) ^{3}}

and passing through

(a_{0}, \frac{12}{( 2 sin ( a _{0} ) + 6 cos ( a _{0} ) ) ^{2}}) : y = - \frac{24 ( 2 cos ( a _{0} ) - 6 sin ( a _{0} ) )}{( 2 sin ( a _{0} ) + 6 cos ( a _{0} ) ) ^{3}} x + \frac{12}{( 2 sin ( a _{0} ) + 6 cos ( a _{0} ) ) ^{2}} + \frac{24 a _{0} ( 2 cos ( a _{0} ) - 6 sin ( a _{0} ) )}{( 2 sin ( a _{0} ) + 6 cos ( a _{0} ) ) ^{3}}

y = - \frac{24 ( 2 cos ( a _{0} ) - 6 sin ( a _{0} ) )}{( 2 sin ( a _{0} ) + 6 cos ( a _{0} ) ) ^{3}} x + \frac{12}{( 2 sin ( a _{0} ) + 6 cos ( a _{0} ) ) ^{2}} + \frac{24 a _{0} ( 2 cos ( a _{0} ) - 6 sin ( a _{0} ) )}{( 2 sin ( a _{0} ) + 6 cos ( a _{0} ) ) ^{3}}

\int_{2}^{3} \frac{11}{3 - x} d x

y^{^{''}} - 6 y^{^{'}} + 9 y = t, y (0) = 0, y^{^{'}} (0) = 1

\frac{d}{d x} (\frac{1}{x} - \frac{1}{sin ( x )})

\frac{d y}{d x} = \frac{6 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2}}{x ^{3} y}

x \to 0 + lim (- x)

What is the tangent of (12)/((2sin(x)+6cos(x))^2) ?
The tangent of (12)/((2sin(x)+6cos(x))^2) is