What is the tangent of 2/(sqrt(x+5)) ?

The tangent of 2/(sqrt(x+5)) is y=-1/((a_{0)+5)^{3/2}}x+(3a_{0}+10)/((a_{0)+5)^{3/2}}

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tangent of 2/(sqrt(x+5))

tangent of

\frac{2}{x + 5}

y = - \frac{1}{( a _{0} + 5 ) ^{\frac{3}{2}}} x + \frac{3 a _{0} + 10}{( a _{0} + 5 ) ^{\frac{3}{2}}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{2}{a _{0} + 5})

Find the slope of

y = \frac{2}{x + 5} : \frac{d y}{d x} = - \frac{1}{( x + 5 ) ^{\frac{3}{2}}}

Compute the slope of

y = \frac{2}{x + 5}

x = a_{0} : m = - \frac{1}{( a _{0} + 5 ) ^{\frac{3}{2}}}

Find the line with slope m=

- \frac{1}{( a _{0} + 5 ) ^{\frac{3}{2}}}

and passing through

(a_{0}, \frac{2}{a _{0} + 5}) : y = - \frac{1}{( a _{0} + 5 ) ^{\frac{3}{2}}} x + \frac{3 a _{0} + 10}{( a _{0} + 5 ) ^{\frac{3}{2}}}

y = - \frac{1}{( a _{0} + 5 ) ^{\frac{3}{2}}} x + \frac{3 a _{0} + 10}{( a _{0} + 5 ) ^{\frac{3}{2}}}

(- 1, - 4), (5, - 4)

\frac{d}{d x} (4 x - 5 x^{\frac{7}{8}})

f (x) = 8 e^{x} + x, (0, 8)

\int_{1}^{e^{2}} \frac{ln ^{3} ( x ^{2} )}{x} d x

n = 0 \sum \infty \frac{n !}{1 0 ^{n}}

What is the tangent of 2/(sqrt(x+5)) ?
The tangent of 2/(sqrt(x+5)) is y=-1/((a_{0)+5)^{3/2}}x+(3a_{0}+10)/((a_{0)+5)^{3/2}}