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

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

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

tangent of

f (x) = 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

f (x) = e^{5 x} : \frac{df ( x )}{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)

x \to 4 - lim (\frac{1 - x}{4 - x})

\int x ln (9 x) d x

x \to 2 lim (x^{2} + 4)

\frac{d}{d x} (x e^{c o s (2 x - y)})

x \to + 3 + lim (\frac{x + 3}{x - 3})

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