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Popular >

derivative of x^2e^{-x}+(ln(x)^2)

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Popular Examples

integral from 0 to 1/2 of xln(2x)

\int_{0}^{\frac{1}{2}} x ln (2 x) d x

derivative of 14x^{1/7}

\frac{d}{d x} (14 x^{\frac{1}{7}})

sum from n=0 to infinity of ((3x-2)^n)/n

n = 0 \sum \infty \frac{( 3 x - 2 ) ^{n}}{n}

y^{''}-4y=(x^2-5)sin(2x)

y^{^{''}} - 4 y = (x^{2} - 5) sin (2 x)

sum from n=1 to infinity of-5/n

n = 1 \sum \infty - \frac{5}{n}

Frequently Asked Questions (FAQ)

What is the derivative of x^2e^{-x}+(ln(x)^2) ?
The derivative of x^2e^{-x}+(ln(x)^2) is 2e^{-x}x-e^{-x}x^2+(2ln(x))/x
What is the first derivative of x^2e^{-x}+(ln(x)^2) ?
The first derivative of x^2e^{-x}+(ln(x)^2) is 2e^{-x}x-e^{-x}x^2+(2ln(x))/x