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Popular >

derivative of (x+1^2e^x)

Solution

\frac{d}{d x} ((x + 1)^{2} e^{x})

Solution

e^{x} x^{2} + 4 e^{x} x + 3 e^{x}

Solution steps

\frac{d}{d x} ((x + 1)^{2} e^{x})

Apply the Product Rule:

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

f = (x + 1)^{2}, g = e^{x}

= \frac{d}{d x} ((x + 1)^{2}) e^{x} + \frac{d}{d x} (e^{x}) (x + 1)^{2}

\frac{d}{d x} ((x + 1)^{2}) = 2 (x + 1)

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

= 2 (x + 1) e^{x} + e^{x} (x + 1)^{2}

Simplify

2 (x + 1) e^{x} + e^{x} (x + 1)^{2} : e^{x} x^{2} + 4 e^{x} x + 3 e^{x}

= e^{x} x^{2} + 4 e^{x} x + 3 e^{x}

Popular Examples

limit as x approaches 9 of \sqrt[4]{9-x}

limit as x approaches (9pi)/2 of sec(x)

x \to \frac{9 π}{2} lim (sec (x))

derivative of ln(1/(x^3+3))

\frac{d}{d x} (ln (\frac{1}{x ^{3} + 3}))

4 y^{2} y d x + x y d y = 0

(\partial)/(\partial x)(ln(9ye^{xy}))

\frac{\partial}{\partial x} (ln (9 y e^{x y}))

Frequently Asked Questions (FAQ)

What is the derivative of (x+1^2e^x) ?
The derivative of (x+1^2e^x) is e^xx^2+4e^xx+3e^x
What is the first derivative of (x+1^2e^x) ?
The first derivative of (x+1^2e^x) is e^xx^2+4e^xx+3e^x