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Popular >

derivative of x^3e^{-x}+ln(2x)

Solution

\frac{d}{d x} (x^{3} e^{- x} + ln (2 x))

Solution

3 e^{- x} x^{2} - e^{- x} x^{3} + \frac{1}{x}

Solution steps

\frac{d}{d x} (x^{3} e^{- x} + ln (2 x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{3} e^{- x}) + \frac{d}{d x} (ln (2 x))

\frac{d}{d x} (x^{3} e^{- x}) = 3 e^{- x} x^{2} - e^{- x} x^{3}

\frac{d}{d x} (ln (2 x)) = \frac{1}{x}

= 3 e^{- x} x^{2} - e^{- x} x^{3} + \frac{1}{x}

Popular Examples

tangent of f(x)=2e^xcos(x),(0,2)tangent of

f (x) = 2 e^{x} cos (x), (0, 2)

derivative of 1/(3x-2)derivative of

\frac{1}{3 x - 2}

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n = 0 \sum \infty (\frac{- 1}{5})^{n}

(\partial)/(\partial x)(5e^{6x})

\frac{\partial}{\partial x} (5 e^{6 x})

integral from 0 to 7 of (7-x)^2

\int_{0}^{7} (7 - x)^{2} d x

Frequently Asked Questions (FAQ)

What is the derivative of x^3e^{-x}+ln(2x) ?
The derivative of x^3e^{-x}+ln(2x) is 3e^{-x}x^2-e^{-x}x^3+1/x
What is the first derivative of x^3e^{-x}+ln(2x) ?
The first derivative of x^3e^{-x}+ln(2x) is 3e^{-x}x^2-e^{-x}x^3+1/x