What is the tangent of f(x)= 3/((x+5)^2),\at x= 3/16 ?

The tangent of f(x)= 3/((x+5)^2),\at x= 3/16 is y=-24576/571787 x+68352/571787

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tangent of f(x)= 3/((x+5)^2),\at x= 3/16

tangent of

f (x) = \frac{3}{( x + 5 ) ^{2}}, at x = \frac{3}{16}

y = - \frac{24576}{571787} x + \frac{68352}{571787}

Solution steps

Find the tangent point:

(\frac{3}{16}, \frac{768}{6889})

Find the slope of

f (x) = \frac{3}{( x + 5 ) ^{2}} : \frac{df ( x )}{d x} = - \frac{6}{( x + 5 ) ^{3}}

Compute the slope of

f (x) = \frac{3}{( x + 5 ) ^{2}}

x = \frac{3}{16} : m = - \frac{24576}{571787}

Find the line with slope m=

- \frac{24576}{571787}

and passing through

(\frac{3}{16}, \frac{768}{6889}) : y = - \frac{24576}{571787} x + \frac{68352}{571787}

y = - \frac{24576}{571787} x + \frac{68352}{571787}

\frac{\partial}{\partial y} (\frac{5 x}{6 y})

(cot (x))^{^{'}}

\frac{\partial}{\partial x} (tan (3 x - 4 y))

\int \frac{3}{u ^{2} + 2} d u

f (x) = (2 x - x^{2})^{3}

What is the tangent of f(x)= 3/((x+5)^2),\at x= 3/16 ?
The tangent of f(x)= 3/((x+5)^2),\at x= 3/16 is y=-24576/571787 x+68352/571787