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}}}

Compute the slope of

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

x = 3 : 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

x \to - 4 lim (- (x^{2} + 10 x + 8))

f (x) = \frac{3}{( 2 x ) ^{2}}

f (x) = tan (x), (\frac{3 π}{4}, - 1)

x \to 2 π lim (csc (x))

9 - x^{2}

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