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Popular >

derivative of f(x)=(x+1)e^x

Solution

derivative of

f (x) = (x + 1) e^{x}

Solution

e^{x} x + 2 e^{x}

Solution steps

\frac{d}{d x} ((x + 1) e^{x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + 1, g = e^{x}

= \frac{d}{d x} (x + 1) e^{x} + \frac{d}{d x} (e^{x}) (x + 1)

\frac{d}{d x} (x + 1) = 1

\frac{d}{d x} (e^{x}) = e^{x}

= 1 \cdot e^{x} + e^{x} (x + 1)

Simplify

1 \cdot e^{x} + e^{x} (x + 1) : e^{x} x + 2 e^{x}

= e^{x} x + 2 e^{x}

Popular Examples

area x^2+1,5 area

x^{2} + 1, 5

derivative of sqrt(x^2+11)derivative of

x^{2} + 11

derivative of c/x+(2a)/(x^3)+8 derivative of

\frac{c}{x} + \frac{2 a}{x ^{3}} + 8

derivative of 2/2

\frac{d}{d x} (\frac{2}{2})

tangent of f(x)=(3x)/(x^2-6),\at x=3 tangent of

f (x) = \frac{3 x}{x ^{2} - 6}, at x = 3

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x+1)e^x ?
The derivative of f(x)=(x+1)e^x is e^xx+2e^x
What is the first derivative of f(x)=(x+1)e^x ?
The first derivative of f(x)=(x+1)e^x is e^xx+2e^x