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}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : 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)

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)