What is the tangent of y=e^{5x},\at x= 1/5 ln(3) ?

The tangent of y=e^{5x},\at x= 1/5 ln(3) is y=15x+3-3ln(3)

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tangent of y=e^{5x},\at x= 1/5 ln(3)

tangent of

y = e^{5 x}, at x = \frac{1}{5} ln (3)

y = 15 x + 3 - 3 ln (3)

Solution steps

Find the tangent point:

(\frac{1}{5} ln (3), 3)

Find the slope of

y = e^{5 x} : \frac{d y}{d x} = e^{5 x} \cdot 5

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 = 15

Find the line with slope m=

15

and passing through

(\frac{1}{5} ln (3), 3) : y = 15 x + 3 - 3 ln (3)

y = 15 x + 3 - 3 ln (3)

What is the tangent of y=e^{5x},\at x= 1/5 ln(3) ?
The tangent of y=e^{5x},\at x= 1/5 ln(3) is y=15x+3-3ln(3)