What is the tangent of sqrt(7x+2) ?

The tangent of sqrt(7x+2) is y= 7/(2sqrt(7a_{0)+2)}x+sqrt(7a_{0)+2}-(7a_{0})/(2sqrt(7a_{0)+2)}

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tangent of sqrt(7x+2)

tangent of

7 x + 2

y = \frac{7}{2 7 a _{0} + 2} x + 7 a_{0} + 2 - \frac{7 a _{0}}{2 7 a _{0} + 2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 7 a_{0} + 2)

Find the slope of

y = 7 x + 2 : \frac{d y}{d x} = \frac{7}{2 7 x + 2}

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{7}{2 7 a _{0} + 2}

Find the line with slope m=

\frac{7}{2 7 a _{0} + 2}

and passing through

(a_{0}, 7 a_{0} + 2) : y = \frac{7}{2 7 a _{0} + 2} x + 7 a_{0} + 2 - \frac{7 a _{0}}{2 7 a _{0} + 2}

y = \frac{7}{2 7 a _{0} + 2} x + 7 a_{0} + 2 - \frac{7 a _{0}}{2 7 a _{0} + 2}

\frac{d}{d x} (ln (\frac{a - x}{a + x}))

5 x^{2} + 2

\frac{d x}{d t} = \frac{x + t}{t}

\frac{d}{d x} (x^{5} + b x^{4} + c x^{3} - 2 x + 1)

(1 + x)^{- \frac{5}{2}}

What is the tangent of sqrt(7x+2) ?
The tangent of sqrt(7x+2) is y= 7/(2sqrt(7a_{0)+2)}x+sqrt(7a_{0)+2}-(7a_{0})/(2sqrt(7a_{0)+2)}