What is the derivative of 5x^7e^x ?

The derivative of 5x^7e^x is 5(7x^6e^x+e^xx^7)

What is the first derivative of 5x^7e^x ?

The first derivative of 5x^7e^x is 5(7x^6e^x+e^xx^7)

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\frac{d}{d x} (5 x^{7} e^{x})

5 (7 x^{6} e^{x} + e^{x} x^{7})

Solution steps

\frac{d}{d x} (5 x^{7} e^{x})

Take the constant out:

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

= 5 \frac{d}{d x} (x^{7} e^{x})

Apply the Product Rule:

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

f = x^{7}, g = e^{x}

= 5 (\frac{d}{d x} (x^{7}) e^{x} + \frac{d}{d x} (e^{x}) x^{7})

\frac{d}{d x} (x^{7}) = 7 x^{6}

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

= 5 (7 x^{6} e^{x} + e^{x} x^{7})

y^{^{'}} = 5 x + y, y (0) = 6

\int l x d x

x^{l n (3)}

\int \frac{3 x - 18}{( x - 9 ) ( x - 5 ) ^{2}} d x

\frac{d y}{d t} = 3 y + y^{3}

What is the derivative of 5x^7e^x ?
The derivative of 5x^7e^x is 5(7x^6e^x+e^xx^7)
What is the first derivative of 5x^7e^x ?
The first derivative of 5x^7e^x is 5(7x^6e^x+e^xx^7)