What is the tangent of sqrt(x^2+11),\at x=5 ?

The tangent of sqrt(x^2+11),\at x=5 is y= 5/6 x+11/6

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tangent of sqrt(x^2+11),\at x=5

tangent of

x^{2} + 11, at x = 5

y = \frac{5}{6} x + \frac{11}{6}

Solution steps

Find the tangent point:

(5, 6)

Find the slope of

y = x^{2} + 11 : \frac{d y}{d x} = \frac{x}{x ^{2} + 11}

Compute the slope of

y = x^{2} + 11

x = 5 : m = \frac{5}{6}

Find the line with slope m=

\frac{5}{6}

and passing through

(5, 6) : y = \frac{5}{6} x + \frac{11}{6}

y = \frac{5}{6} x + \frac{11}{6}

t^{13 t}

\frac{d}{d x} (sec (5 x) + 1)

f (x) = 4 x^{\frac{5}{4}} + 4 x^{\frac{3}{2}} + 8 x

(x - 1)^{3} \frac{d y}{d x} + 4 (x - 1)^{2} y = x + 1

y^{^{'}} = - \frac{1 + x + y}{1 + x}

What is the tangent of sqrt(x^2+11),\at x=5 ?
The tangent of sqrt(x^2+11),\at x=5 is y= 5/6 x+11/6