What is the tangent of y=(sqrt(5))^x,\at x=6 ?

The tangent of y=(sqrt(5))^x,\at x=6 is y=(125ln(5))/2 x+125-375ln(5)

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tangent of y=(sqrt(5))^x,\at x=6

tangent of

y = (5)^{x}, at x = 6

y = \frac{125 ln ( 5 )}{2} x + 125 - 375 ln (5)

Solution steps

Find the tangent point:

(6, 125)

Find the slope of

y = (5)^{x} : \frac{d y}{d x} = \frac{1}{2} ln (5) e^{\frac{l n ( 5 ) x}{2}}

Compute the slope of

y = (5)^{x}

x = 6 : m = \frac{125 ln ( 5 )}{2}

Find the line with slope m=

\frac{125 ln ( 5 )}{2}

and passing through

(6, 125) : y = \frac{125 ln ( 5 )}{2} x + 125 - 375 ln (5)

y = \frac{125 ln ( 5 )}{2} x + 125 - 375 ln (5)

x \to - 2 lim (\frac{- 1}{( x + 2 )})

\frac{d}{d x} ((2 x - 1)^{3} (x + 1)^{5})

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

\frac{3 - 2 x + 5}{x - 2}

x \to 0 lim (x^{2} + 2 x + 1)

What is the tangent of y=(sqrt(5))^x,\at x=6 ?
The tangent of y=(sqrt(5))^x,\at x=6 is y=(125ln(5))/2 x+125-375ln(5)