What is the tangent of sqrt((3x+25)) ?

The tangent of sqrt((3x+25)) is y= 3/(2sqrt(3a_{0)+25)}x+sqrt(3a_{0)+25}-(3a_{0})/(2sqrt(3a_{0)+25)}

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tangent of sqrt((3x+25))

tangent of

(3 x + 25)

y = \frac{3}{2 3 a _{0} + 25} x + 3 a_{0} + 25 - \frac{3 a _{0}}{2 3 a _{0} + 25}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 3 a_{0} + 25)

Find the slope of

y = 3 x + 25 : \frac{d y}{d x} = \frac{3}{2 3 x + 25}

Compute the slope of

y = 3 x + 25

x = a_{0} : m = \frac{3}{2 3 a _{0} + 25}

Find the line with slope m=

\frac{3}{2 3 a _{0} + 25}

and passing through

(a_{0}, 3 a_{0} + 25) : y = \frac{3}{2 3 a _{0} + 25} x + 3 a_{0} + 25 - \frac{3 a _{0}}{2 3 a _{0} + 25}

y = \frac{3}{2 3 a _{0} + 25} x + 3 a_{0} + 25 - \frac{3 a _{0}}{2 3 a _{0} + 25}

\frac{\partial}{\partial x} (e^{2 x} cos (y))

x \to - 2 lim (3 x + 4)

\int x e^{5 x} d x

h \to 0 lim (\frac{1}{h ^{2}})

\int x n (x) d x

What is the tangent of sqrt((3x+25)) ?
The tangent of sqrt((3x+25)) is y= 3/(2sqrt(3a_{0)+25)}x+sqrt(3a_{0)+25}-(3a_{0})/(2sqrt(3a_{0)+25)}