What is the tangent of 5/(sqrt(x)),\at x=a ?

The tangent of 5/(sqrt(x)),\at x=a is y=-5/(2a^{3/2)}x+(15)/(2sqrt(a))

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tangent of 5/(sqrt(x)),\at x=a

tangent of

\frac{5}{x}, at x = a

y = - \frac{5}{2 a ^{\frac{3}{2}}} x + \frac{15}{2 a}

Solution steps

Find the tangent point:

(a, \frac{5}{a})

Find the slope of

y = \frac{5}{x} : \frac{d y}{d x} = - \frac{5}{2 x ^{\frac{3}{2}}}

Compute the slope of

y = \frac{5}{x}

x = a : m = - \frac{5}{2 a ^{\frac{3}{2}}}

Find the line with slope m=

- \frac{5}{2 a ^{\frac{3}{2}}}

and passing through

(a, \frac{5}{a}) : y = - \frac{5}{2 a ^{\frac{3}{2}}} x + \frac{15}{2 a}

y = - \frac{5}{2 a ^{\frac{3}{2}}} x + \frac{15}{2 a}

\int \frac{1}{x ^{3} ( ( x ^{2} - 9 ) )} d x

\frac{d}{d x} ((e^{x} - 1)^{2})

\int 2 x (x^{2} + 3)^{6} d x

\frac{1}{u ^{\frac{1}{2}}}

\frac{\partial}{\partial x} (x^{\frac{y}{y + z}})

What is the tangent of 5/(sqrt(x)),\at x=a ?
The tangent of 5/(sqrt(x)),\at x=a is y=-5/(2a^{3/2)}x+(15)/(2sqrt(a))