What is (\partial)/(\partial x)(-7x^2e^{6x}) ?

The answer to (\partial)/(\partial x)(-7x^2e^{6x}) is -7(2xe^{6x}+e^{6x}*6x^2)

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(\partial)/(\partial x)(-7x^2e^{6x})

\frac{\partial}{\partial x} (- 7 x^{2} e^{6 x})

- 7 (2 x e^{6 x} + e^{6 x} \cdot 6 x^{2})

Solution steps

\frac{\partial}{\partial x} (- 7 x^{2} e^{6 x})

Take the constant out:

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

= - 7 \frac{\partial}{\partial x} (x^{2} e^{6 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{6 x}

= - 7 (\frac{\partial}{\partial x} (x^{2}) e^{6 x} + \frac{\partial}{\partial x} (e^{6 x}) x^{2})

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (e^{6 x}) = e^{6 x} \cdot 6

= - 7 (2 x e^{6 x} + e^{6 x} \cdot 6 x^{2})

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\int \frac{5 x ^{4} + 6}{( x ^{5} + 6 x ) ^{2}} d x

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What is (\partial)/(\partial x)(-7x^2e^{6x}) ?
The answer to (\partial)/(\partial x)(-7x^2e^{6x}) is -7(2xe^{6x}+e^{6x}*6x^2)