What is the tangent of \sqrt[5]{2x^3+8x}(2.2) ?

The tangent of \sqrt[5]{2x^3+8x}(2.2) is

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tangent of \sqrt[5]{2x^3+8x}(2.2)

tangent of

5 2 x^{3} + 8 x (2.2)

y = \frac{0.44 ( 6 a _{0}^{2} + 8 )}{( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}} x + \frac{220 5 2 a _{0}^{3} + 8 a _{0} ( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}} - 44 a _{0} ( 6 a _{0}^{2} + 8 )}{100 ( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 5 2 a_{0}^{3} + 8 a_{0} \cdot 2.2)

Find the slope of

y = 5 2 x^{3} + 8 x 2.2 : \frac{d y}{d x} = \frac{0.44 ( 6 x ^{2} + 8 )}{( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}}

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 = \frac{0.44 ( 6 a _{0}^{2} + 8 )}{( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}}

Find the line with slope m=

\frac{0.44 ( 6 a _{0}^{2} + 8 )}{( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}}

and passing through

(a_{0}, 5 2 a_{0}^{3} + 8 a_{0} 2.2) : y = \frac{0.44 ( 6 a _{0}^{2} + 8 )}{( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}} x + \frac{220 5 2 a _{0}^{3} + 8 a _{0} ( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}} - 44 a _{0} ( 6 a _{0}^{2} + 8 )}{100 ( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}}

y = \frac{0.44 ( 6 a _{0}^{2} + 8 )}{( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}} x + \frac{220 5 2 a _{0}^{3} + 8 a _{0} ( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}} - 44 a _{0} ( 6 a _{0}^{2} + 8 )}{100 ( 2 a _{0}^{3} + 8 a _{0} ) ^{\frac{4}{5}}}

n \to \infty lim (5 n e^{- n})

n = 1 \sum \infty \frac{4}{2 ^{n}}

\int \frac{x}{1 + x ^{4}} d x

\frac{d}{d x} (5 x y^{2})

\int \frac{1}{x ^{2} - 6 x + 5} d x

What is the tangent of \sqrt[5]{2x^3+8x}(2.2) ?
The tangent of \sqrt[5]{2x^3+8x}(2.2) is