What is the derivative of f(x)=x^6e^x ?

The derivative of f(x)=x^6e^x is 6x^5e^x+e^xx^6

What is the first derivative of f(x)=x^6e^x ?

The first derivative of f(x)=x^6e^x is 6x^5e^x+e^xx^6

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derivative of

f (x) = x^{6} e^{x}

6 x^{5} e^{x} + e^{x} x^{6}

Solution steps

\frac{d}{d x} (x^{6} e^{x})

Apply the Product Rule:

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

f = x^{6}, g = e^{x}

= \frac{d}{d x} (x^{6}) e^{x} + \frac{d}{d x} (e^{x}) x^{6}

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= 6 x^{5} e^{x} + e^{x} x^{6}

y = e^{- 2 x} \cdot tan (8 x)

x \to 0 lim (\frac{3 sin ( 3 x )}{x})

x, sin (x), [\frac{π}{2}, π]

y^{^{''}} + 3 y = 1

(x y - y) d y - (y + 1) d x = 0

What is the derivative of f(x)=x^6e^x ?
The derivative of f(x)=x^6e^x is 6x^5e^x+e^xx^6
What is the first derivative of f(x)=x^6e^x ?
The first derivative of f(x)=x^6e^x is 6x^5e^x+e^xx^6