What is (d^3)/(dx^3)(x^5e^x) ?

The answer to (d^3)/(dx^3)(x^5e^x) is e^xx^5+15e^xx^4+60e^xx^3+60e^xx^2

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(d^3)/(dx^3)(x^5e^x)

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

e^{x} x^{5} + 15 e^{x} x^{4} + 60 e^{x} x^{3} + 60 e^{x} x^{2}

Solution steps

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

\frac{d}{d x} (x^{5} e^{x}) = 5 x^{4} e^{x} + e^{x} x^{5}

= \frac{d ^{2}}{d x ^{2}} (5 x^{4} e^{x} + e^{x} x^{5})

\frac{d}{d x} (5 x^{4} e^{x} + e^{x} x^{5}) = e^{x} x^{5} + 10 e^{x} x^{4} + 20 e^{x} x^{3}

= \frac{d}{d x} (e^{x} x^{5} + 10 e^{x} x^{4} + 20 e^{x} x^{3})

\frac{d}{d x} (e^{x} x^{5} + 10 e^{x} x^{4} + 20 e^{x} x^{3}) = e^{x} x^{5} + 15 e^{x} x^{4} + 60 e^{x} x^{3} + 60 e^{x} x^{2}

= e^{x} x^{5} + 15 e^{x} x^{4} + 60 e^{x} x^{3} + 60 e^{x} x^{2}

\frac{d}{d x} (\frac{4 x ^{2}}{( 7 - 5 x ) ^{3}})

\int \frac{e ^{x}}{4 + e ^{2 x}} d x

\int t (t^{4} + t - 5) d t

\frac{\partial}{\partial x} (2 y - \frac{3}{y ^{2}} + x)

(x^{6} - 5) x

What is (d^3)/(dx^3)(x^5e^x) ?
The answer to (d^3)/(dx^3)(x^5e^x) is e^xx^5+15e^xx^4+60e^xx^3+60e^xx^2