What is the tangent of 3/(2sqrt(3x+13)),\at x=-3 ?

The tangent of 3/(2sqrt(3x+13)),\at x=-3 is y=-9/32 x-3/32

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tangent of 3/(2sqrt(3x+13)),\at x=-3

tangent of

\frac{3}{2 3 x + 13}, at x = - 3

y = - \frac{9}{32} x - \frac{3}{32}

Solution steps

Find the tangent point:

(- 3, \frac{3}{4})

Find the slope of

y = \frac{3}{2 3 x + 13} : \frac{d y}{d x} = - \frac{9}{4 ( 3 x + 13 ) ^{\frac{3}{2}}}

Compute the slope of

y = \frac{3}{2 3 x + 13}

x = - 3 : m = - \frac{9}{32}

Find the line with slope m=

- \frac{9}{32}

and passing through

(- 3, \frac{3}{4}) : y = - \frac{9}{32} x - \frac{3}{32}

y = - \frac{9}{32} x - \frac{3}{32}

x, \frac{d ^{2} x}{d t ^{2}} + x = (t^{2} + t) sin (t)

(- 5, 11), (- 10, 6)

\frac{π}{x}

y^{^{'}} = \frac{y}{50 + t} 5, y (0) = 30

\int 16 x^{3} e^{x^{4} + 1} d x

What is the tangent of 3/(2sqrt(3x+13)),\at x=-3 ?
The tangent of 3/(2sqrt(3x+13)),\at x=-3 is y=-9/32 x-3/32