What is the tangent of 9x^{3/5}-2x^{6/7},\at x=3 ?

The tangent of 9x^{3/5}-2x^{6/7},\at x=3 is

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tangent of 9x^{3/5}-2x^{6/7},\at x=3

tangent of

9 x^{\frac{3}{5}} - 2 x^{\frac{6}{7}}, at x = 3

y = (\frac{9 \cdot 3 ^{\frac{3}{5}}}{5} - \frac{4 \cdot 3 ^{\frac{6}{7}}}{7}) x + 9 \cdot 3^{\frac{3}{5}} - 2 \cdot 3^{\frac{6}{7}} - (\frac{9 \cdot 3 ^{\frac{3}{5}}}{5} - \frac{4 \cdot 3 ^{\frac{6}{7}}}{7}) \cdot 3

Solution steps

Find the tangent point:

(3, 9 \cdot 3^{\frac{3}{5}} - 2 \cdot 3^{\frac{6}{7}})

Find the slope of

y = 9 x^{\frac{3}{5}} - 2 x^{\frac{6}{7}} : \frac{d y}{d x} = \frac{27}{5 x ^{\frac{2}{5}}} - \frac{12}{7 x ^{\frac{1}{7}}}

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{9 \cdot 3 ^{\frac{3}{5}}}{5} - \frac{4 \cdot 3 ^{\frac{6}{7}}}{7}

Find the line with slope m=

\frac{9 \cdot 3 ^{\frac{3}{5}}}{5} - \frac{4 \cdot 3 ^{\frac{6}{7}}}{7}

and passing through

(3, 9 \cdot 3^{\frac{3}{5}} - 2 \cdot 3^{\frac{6}{7}}) : y = (\frac{9 \cdot 3 ^{\frac{3}{5}}}{5} - \frac{4 \cdot 3 ^{\frac{6}{7}}}{7}) x + 9 \cdot 3^{\frac{3}{5}} - 2 \cdot 3^{\frac{6}{7}} - (\frac{9 \cdot 3 ^{\frac{3}{5}}}{5} - \frac{4 \cdot 3 ^{\frac{6}{7}}}{7}) \cdot 3

y = (\frac{9 \cdot 3 ^{\frac{3}{5}}}{5} - \frac{4 \cdot 3 ^{\frac{6}{7}}}{7}) x + 9 \cdot 3^{\frac{3}{5}} - 2 \cdot 3^{\frac{6}{7}} - (\frac{9 \cdot 3 ^{\frac{3}{5}}}{5} - \frac{4 \cdot 3 ^{\frac{6}{7}}}{7}) \cdot 3

What is the tangent of 9x^{3/5}-2x^{6/7},\at x=3 ?
The tangent of 9x^{3/5}-2x^{6/7},\at x=3 is