What is (\partial)/(\partial x)(x^2+16xw+64w^2) ?

The answer to (\partial)/(\partial x)(x^2+16xw+64w^2) is 2x+16w

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(\partial)/(\partial x)(x^2+16xw+64w^2)

\frac{\partial}{\partial x} (x^{2} + 16 x w + 64 w^{2})

2 x + 16 w

Solution steps

\frac{\partial}{\partial x} (x^{2} + 16 x w + 64 w^{2})

Treat

w

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (16 x w) + \frac{\partial}{\partial x} (64 w^{2})

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

\frac{\partial}{\partial x} (16 x w) = 16 w

\frac{\partial}{\partial x} (64 w^{2}) = 0

= 2 x + 16 w + 0

Simplify

= 2 x + 16 w

x \to 3 - lim (\frac{2 x + 1}{x - 3})

x \to 0 - lim (\frac{4}{5 x ^{\frac{1}{3}}})

\int \frac{5}{2} d x

\int_{1}^{\infty} 12 e^{- 4 x} d x

(\frac{t ^{3}}{t ^{8} + 7})^{2}

What is (\partial)/(\partial x)(x^2+16xw+64w^2) ?
The answer to (\partial)/(\partial x)(x^2+16xw+64w^2) is 2x+16w