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Popular >

derivative of 5x^2e^x

Solution

derivative of

5 x^{2} e^{x}

Solution

5 (2 x e^{x} + e^{x} x^{2})

Solution steps

\frac{d}{d x} (5 x^{2} e^{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (x^{2} e^{x})

Apply the Product Rule:

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

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

= 5 (\frac{d}{d x} (x^{2}) e^{x} + \frac{d}{d x} (e^{x}) x^{2})

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

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

= 5 (2 x e^{x} + e^{x} x^{2})

Popular Examples

integral from 0 to 1 of (2x+3)e^{-5x}

\int_{0}^{1} (2 x + 3) e^{- 5 x} d x

derivative of (e^x(x^5+3)/(x^{10)+9})

\frac{d}{d x} (\frac{e ^{x} ( x ^{5} + 3 )}{x ^{10} + 9})

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

\frac{s}{s ^{2} + a ^{2}}

integral of (6x^3+4x^2-47x-27)/(x^2-9)

\int \frac{6 x ^{3} + 4 x ^{2} - 47 x - 27}{x ^{2} - 9} d x

sum from n=0 to infinity of 4^n

n = 0 \sum \infty 4^{n}

Frequently Asked Questions (FAQ)

What is the derivative of 5x^2e^x ?
The derivative of 5x^2e^x is 5(2xe^x+e^xx^2)
What is the first derivative of 5x^2e^x ?
The first derivative of 5x^2e^x is 5(2xe^x+e^xx^2)