What is the tangent of y=(7x-4)(2+6x) ?

The tangent of y=(7x-4)(2+6x) is y=(84a_{0}-10)x-42a_{0}^2-8

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tangent of y=(7x-4)(2+6x)

tangent of

y = (7 x - 4) (2 + 6 x)

y = (84 a_{0} - 10) x - 42 a_{0}^{2} - 8

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, (7 a_{0} - 4) (2 + 6 a_{0}))

Find the slope of

y = (7 x - 4) (2 + 6 x) : \frac{d y}{d x} = 84 x - 10

Compute the slope of

y = (7 x - 4) (2 + 6 x)

x = a_{0} : m = 84 a_{0} - 10

Find the line with slope m=

84 a_{0} - 10

and passing through

(a_{0}, (7 a_{0} - 4) (2 + 6 a_{0})) : y = (84 a_{0} - 10) x - 42 a_{0}^{2} - 8

y = (84 a_{0} - 10) x - 42 a_{0}^{2} - 8

x \to \infty lim (arctan (1 - x))

x \to 0 + lim (arctan (ln (x)))

\frac{d v}{d x} - \frac{1}{x} v = 8

\frac{ln ( x )}{e ^{x}}

x \to 0 lim (\frac{5}{x} - \frac{5}{∣ x ∣})

What is the tangent of y=(7x-4)(2+6x) ?
The tangent of y=(7x-4)(2+6x) is y=(84a_{0}-10)x-42a_{0}^2-8