Question

Finding an Equation of a Tangent Line In Exercise, find an equation of the tangent line to the graph of the function at the given point.
y = xe^x - e^x, (1, 0)

Answer 1

Answer:

Equation of tangent:

$y = xe^{x}$

At point (1,0):

y = 2.713

Step-by-step explanation:

The equation of tangent line to the function can be calculated by taking the first derivative.

We have,

$y = xe^{x}-e^{x}\\\frac{dy}{dx}=\frac{d}{dx}[ xe^{x} ]-\frac{d}{dx} [e^{x}]$

Applying Product Rule:

d/dx [u.v] = (d/dx u) . (v) + (u) . (d/dx v)

Therefore,

$\frac{dy}{dx}=\frac{d}{dx}(x) . e^{x}+x .\frac{d}{dx}(e^{x})- \frac{d}{dx}(e^{x})\\\\\frac{dy}{dx}=(1)(e^{x})+(x)(e^{x})-e^{x}\\ \frac{dy}{dx}=xe^{x}$

The above equation is the equation of tangent line.

The point given is (1,0):

So,

$\frac{dy}{dx} = (1)e^{1}\\ \frac{dy}{dx} = e\\\frac{dy}{dx} = 2.713$