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

The tangent of y=e^{5x},\at x= 1/5 ln(5) is y=25x+5-5ln(5)

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

tangent of

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

y = 25 x + 5 - 5 ln (5)

Solution steps

Find the tangent point:

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

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 = 25

Find the line with slope m=

25

and passing through

(\frac{1}{5} ln (5), 5) : y = 25 x + 5 - 5 ln (5)

y = 25 x + 5 - 5 ln (5)

What is the tangent of y=e^{5x},\at x= 1/5 ln(5) ?
The tangent of y=e^{5x},\at x= 1/5 ln(5) is y=25x+5-5ln(5)