What is the derivative of x^7e^{10x} ?

The derivative of x^7e^{10x} is 7x^6e^{10x}+e^{10x}*10x^7

What is the first derivative of x^7e^{10x} ?

The first derivative of x^7e^{10x} is 7x^6e^{10x}+e^{10x}*10x^7

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\frac{d}{d x} (x^{7} e^{10 x})

7 x^{6} e^{10 x} + e^{10 x} \cdot 10 x^{7}

Solution steps

\frac{d}{d x} (x^{7} e^{10 x})

Apply the Product Rule:

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

f = x^{7}, g = e^{10 x}

= \frac{d}{d x} (x^{7}) e^{10 x} + \frac{d}{d x} (e^{10 x}) x^{7}

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

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

= 7 x^{6} e^{10 x} + e^{10 x} \cdot 10 x^{7}

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

y^{^{''}} - 30 y^{^{'}} + 225 y = 0

y \to \frac{1}{2} lim ((16 y^{2} - 4)^{4})

x \to o lim (x^{x})

\frac{d}{d y} (2 x y^{4} e^{y})

What is the derivative of x^7e^{10x} ?
The derivative of x^7e^{10x} is 7x^6e^{10x}+e^{10x}*10x^7
What is the first derivative of x^7e^{10x} ?
The first derivative of x^7e^{10x} is 7x^6e^{10x}+e^{10x}*10x^7