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Popular >

derivative of e^x(x-2^2)

Solution

\frac{d}{d x} (e^{x} (x - 2)^{2})

Solution

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

Solution steps

\frac{d}{d x} (e^{x} (x - 2)^{2})

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((x - 2)^{2}) = 2 (x - 2)

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

Simplify

e^{x} (x - 2)^{2} + 2 (x - 2) e^{x} : e^{x} x^{2} - 2 e^{x} x

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

Popular Examples

derivative of y=ln(sqrt(a-1))derivative of

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\int \frac{x ^{2} + 6 x + 6}{x ^{3} + 9 x ^{2} + 18 x + 7} d x

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\frac{d}{d x} (\frac{54}{( 3 x + 1 ) ^{4}})

x^2y^'+2xy=9cos^2(x)

x^{2} y^{^{'}} + 2 x y = 9 cos^{2} (x)

(\partial)/(\partial t)(x^2sin(3t))

\frac{\partial}{\partial t} (x^{2} sin (3 t))

Frequently Asked Questions (FAQ)

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