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Popular >

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

Solution

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

Solution

e^{x} (1 - x^{2}) - 2 e^{x} x

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = 1 - x^{2}

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

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

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

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

Simplify

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

Popular Examples

derivative of f(x)= 8/(sqrt(x))derivative of

f (x) = \frac{8}{x}

xy^'=3x^3y^{1/2}-2y

x y^{^{'}} = 3 x^{3} y^{\frac{1}{2}} - 2 y

inverse oflaplace s/((s+1)^2+1)inverse laplace

\frac{s}{( s + 1 ) ^{2} + 1}

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\frac{d}{d x} ((x - x + 6 x^{4})^{3})

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\int (x^{3} (1 + x^{2}))^{- 1} d x

Frequently Asked Questions (FAQ)

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