What is the tangent of (3x+6)^{1/5},\at x=2 ?

The tangent of (3x+6)^{1/5},\at x=2 is y=(3^{1/5})/(10*2^{3/5)}x+12^{1/5}-(3^{1/5})/(5*2^{3/5)}

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tangent of (3x+6)^{1/5},\at x=2

tangent of

(3 x + 6)^{\frac{1}{5}}, at x = 2

y = \frac{3 ^{\frac{1}{5}}}{10 \cdot 2 ^{\frac{3}{5}}} x + 1 2^{\frac{1}{5}} - \frac{3 ^{\frac{1}{5}}}{5 \cdot 2 ^{\frac{3}{5}}}

Solution steps

Find the tangent point:

(2, 1 2^{\frac{1}{5}})

Find the slope of

y = (3 x + 6)^{\frac{1}{5}} : \frac{d y}{d x} = \frac{3}{5 ( 3 x + 6 ) ^{\frac{4}{5}}}

Compute the slope of

y = (3 x + 6)^{\frac{1}{5}}

x = 2 : m = \frac{3 ^{\frac{1}{5}}}{10 \cdot 2 ^{\frac{3}{5}}}

Find the line with slope m=

\frac{3 ^{\frac{1}{5}}}{10 \cdot 2 ^{\frac{3}{5}}}

and passing through

(2, 1 2^{\frac{1}{5}}) : y = \frac{3 ^{\frac{1}{5}}}{10 \cdot 2 ^{\frac{3}{5}}} x + 1 2^{\frac{1}{5}} - \frac{3 ^{\frac{1}{5}}}{5 \cdot 2 ^{\frac{3}{5}}}

y = \frac{3 ^{\frac{1}{5}}}{10 \cdot 2 ^{\frac{3}{5}}} x + 1 2^{\frac{1}{5}} - \frac{3 ^{\frac{1}{5}}}{5 \cdot 2 ^{\frac{3}{5}}}

\frac{\partial}{\partial x} (x^{2} y^{2} e^{4 x y})

\frac{d}{d x} ((x \cdot sinh (x) + cos (x))^{5})

\frac{d}{d x} (\frac{x + 6}{x ^{3} + x - 8})

x^{2} - 2 x - 1

\frac{( s + 4 )}{s ^{2} + 4 s + 29}

What is the tangent of (3x+6)^{1/5},\at x=2 ?
The tangent of (3x+6)^{1/5},\at x=2 is y=(3^{1/5})/(10*2^{3/5)}x+12^{1/5}-(3^{1/5})/(5*2^{3/5)}