What is the derivative of y=5x^{10}e^x ?

The derivative of y=5x^{10}e^x is 5(10x^9e^x+e^xx^{10})

What is the first derivative of y=5x^{10}e^x ?

The first derivative of y=5x^{10}e^x is 5(10x^9e^x+e^xx^{10})

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derivative of

y = 5 x^{10} e^{x}

5 (10 x^{9} e^{x} + e^{x} x^{10})

Solution steps

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

Take the constant out:

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

= 5 \frac{d}{d x} (x^{10} e^{x})

Apply the Product Rule:

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

f = x^{10}, g = e^{x}

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

\frac{d}{d x} (x^{10}) = 10 x^{9}

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

= 5 (10 x^{9} e^{x} + e^{x} x^{10})

\int x sin (4) x^{2} d x

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f (t) = t^{2} - 2 t

y^{^{''''}} + 32 y^{^{''}} + 256 y = 0

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What is the derivative of y=5x^{10}e^x ?
The derivative of y=5x^{10}e^x is 5(10x^9e^x+e^xx^{10})
What is the first derivative of y=5x^{10}e^x ?
The first derivative of y=5x^{10}e^x is 5(10x^9e^x+e^xx^{10})