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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} - 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} - e^{x}

= e^{x} x^{2} - e^{x}

Popular Examples

integral of ((x+1))/(x^2+2x+2)

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

derivative of ln((1+sin(4x)/(cos(4x))))

\frac{d}{d x} (ln (\frac{1 + sin ( 4 x )}{cos ( 4 x )}))

derivative of sqrt(4ax)

\frac{d}{d x} (4 a x)

integral of 4x^3e^{4x^4}

\int 4 x^{3} e^{4 x^{4}} d x

derivative of y=-5/2 x+3 derivative of

y = - \frac{5}{2} x + 3

Frequently Asked Questions (FAQ)

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