Question
Asked Nov 27, 2019
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Find an equation of the tangent line to the graph of the function at the given point.

f(x) = ex ln(x),    (1, 0)
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Expert Answer

Step 1

Refer to the question we need to find an equation of the tangent line to the graph of the provided function at the given point.

In (x). point (1,0)
f(x)e
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In (x). point (1,0) f(x)e

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Step 2

Use the product rule of derivative as,

uf(x)v=g(x)
(n)p
dx
dv)d(u)
Product rule: f'(uv) =u-
dx
d(e)
dx
d(In x) 1
dx
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uf(x)v=g(x) (n)p dx dv)d(u) Product rule: f'(uv) =u- dx d(e) dx d(In x) 1 dx

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Step 3

To find the equation of tangent line to the graph fin...

f(x)e In (x)
{n x(-e")}
1
f'(x)e
(x)=nx)
'(x)=
-In x e
х
At point (1,0)
1
f'(1) e)
hn (1).е 1)
f(1)
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f(x)e In (x) {n x(-e")} 1 f'(x)e (x)=nx) '(x)= -In x e х At point (1,0) 1 f'(1) e) hn (1).е 1) f(1)

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Tagged in

Math

Calculus