What is the tangent of x^{1/3+y^{1/3}}=7 ?

The tangent of x^{1/3+y^{1/3}}=7 is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tangent of x^{1/3+y^{1/3}}=7

tangent of

x^{\frac{1}{3} + y^{\frac{1}{3}}} = 7

y = (\frac{2 ln ^{2} ( 7 )}{a _{0} ln ^{3} ( a _{0} )} - \frac{3 ln ^{3} ( 7 )}{a _{0} ln ^{4} ( a _{0} )} - \frac{ln ( 7 )}{3 a _{0} ln ^{2} ( a _{0} )}) x + \frac{ln ^{3} ( 7 ) - 2 ln ^{2} ( 7 )}{ln ^{3} ( a _{0} )} - \frac{ln ^{2} ( 7 )}{ln ^{2} ( a _{0} )} + \frac{ln ( 7 )}{3 ln ( a _{0} )} - \frac{1}{27} + \frac{3 ln ^{3} ( 7 )}{ln ^{4} ( a _{0} )} + \frac{ln ( 7 )}{3 ln ^{2} ( a _{0} )}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{ln ^{3} ( 7 )}{ln ^{3} ( a _{0} )} - \frac{ln ^{2} ( 7 )}{ln ^{2} ( a _{0} )} + \frac{ln ( 7 )}{3 ln ( a _{0} )} - \frac{1}{27})

Find the slope of

x^{\frac{1}{3} + y^{\frac{1}{3}}} = 7 : \frac{d y}{d x} = \frac{2 ln ^{2} ( 7 )}{x ln ^{3} ( x )} - \frac{3 ln ^{3} ( 7 )}{x ln ^{4} ( x )} - \frac{ln ( 7 )}{3 x ln ^{2} ( x )}

Compute the slope of

x^{\frac{1}{3} + y^{\frac{1}{3}}} = 7

x = a_{0} : m = \frac{2 ln ^{2} ( 7 )}{a _{0} ln ^{3} ( a _{0} )} - \frac{3 ln ^{3} ( 7 )}{a _{0} ln ^{4} ( a _{0} )} - \frac{ln ( 7 )}{3 a _{0} ln ^{2} ( a _{0} )}

Find the line with slope m=

\frac{2 ln ^{2} ( 7 )}{a _{0} ln ^{3} ( a _{0} )} - \frac{3 ln ^{3} ( 7 )}{a _{0} ln ^{4} ( a _{0} )} - \frac{ln ( 7 )}{3 a _{0} ln ^{2} ( a _{0} )}

and passing through

(a_{0}, \frac{ln ^{3} ( 7 )}{ln ^{3} ( a _{0} )} - \frac{ln ^{2} ( 7 )}{ln ^{2} ( a _{0} )} + \frac{ln ( 7 )}{3 ln ( a _{0} )} - \frac{1}{27}) : y = (\frac{2 ln ^{2} ( 7 )}{a _{0} ln ^{3} ( a _{0} )} - \frac{3 ln ^{3} ( 7 )}{a _{0} ln ^{4} ( a _{0} )} - \frac{ln ( 7 )}{3 a _{0} ln ^{2} ( a _{0} )}) x + \frac{ln ^{3} ( 7 ) - 2 ln ^{2} ( 7 )}{ln ^{3} ( a _{0} )} - \frac{ln ^{2} ( 7 )}{ln ^{2} ( a _{0} )} + \frac{ln ( 7 )}{3 ln ( a _{0} )} - \frac{1}{27} + \frac{3 ln ^{3} ( 7 )}{ln ^{4} ( a _{0} )} + \frac{ln ( 7 )}{3 ln ^{2} ( a _{0} )}

y = (\frac{2 ln ^{2} ( 7 )}{a _{0} ln ^{3} ( a _{0} )} - \frac{3 ln ^{3} ( 7 )}{a _{0} ln ^{4} ( a _{0} )} - \frac{ln ( 7 )}{3 a _{0} ln ^{2} ( a _{0} )}) x + \frac{ln ^{3} ( 7 ) - 2 ln ^{2} ( 7 )}{ln ^{3} ( a _{0} )} - \frac{ln ^{2} ( 7 )}{ln ^{2} ( a _{0} )} + \frac{ln ( 7 )}{3 ln ( a _{0} )} - \frac{1}{27} + \frac{3 ln ^{3} ( 7 )}{ln ^{4} ( a _{0} )} + \frac{ln ( 7 )}{3 ln ^{2} ( a _{0} )}

y^{^{''}} - 2 y^{^{'}} + 17 y = 0

x \to 1 lim (\frac{- 1}{x})

x \to 0 + lim ((x + 1)^{I n (x)})

\frac{d}{d x} (- 5 sin (x) (x + 3 sin (x)))

(x^{9} - 2)^{3}