What is the tangent of y=6^x,\at x=1 ?

The tangent of y=6^x,\at x=1 is y=6ln(6)x+6-6ln(6)

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tangent of y=6^x,\at x=1

tangent

y = 6 ln (6) x + 6 - 6 ln (6)

Solution steps

Find the tangent point:

(1, 6)

Find the slope of

y = 6^{x} : \frac{d y}{d x} = 6^{x} ln (6)

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 = 6 ln (6)

Find the line with slope m=

6 ln (6)

and passing through

(1, 6) : y = 6 ln (6) x + 6 - 6 ln (6)

y = 6 ln (6) x + 6 - 6 ln (6)

What is the tangent of y=6^x,\at x=1 ?
The tangent of y=6^x,\at x=1 is y=6ln(6)x+6-6ln(6)