What is (\partial)/(\partial x)((4x+4)(ln(8xy))) ?

The answer to (\partial)/(\partial x)((4x+4)(ln(8xy))) is 4ln(8xy)+(4x+4)/x

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(\partial)/(\partial x)((4x+4)(ln(8xy)))

\frac{\partial}{\partial x} ((4 x + 4) (ln (8 x y)))

4 ln (8 x y) + \frac{4 x + 4}{x}

Solution steps

\frac{\partial}{\partial x} ((4 x + 4) (ln (8 x y)))

Treat

y

as a constant

Apply the Product Rule:

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

f = 4 x + 4, g = ln (8 x y)

= \frac{\partial}{\partial x} (4 x + 4) ln (8 x y) + \frac{\partial}{\partial x} (ln (8 x y)) (4 x + 4)

\frac{\partial}{\partial x} (4 x + 4) = 4

\frac{\partial}{\partial x} (ln (8 x y)) = \frac{1}{x}

= 4 ln (8 x y) + \frac{1}{x} (4 x + 4)

\frac{1}{x} (4 x + 4) = \frac{4 x + 4}{x}

= 4 ln (8 x y) + \frac{4 x + 4}{x}

\frac{d}{d x} (A x^{2} e^{- 2 x})

\int (sec^{2} (x) - 5) d x

f (x) = (1 + 5 x)^{9}, at x = 0

x \to 0 + lim (\frac{I n x}{x})

\frac{d y}{d x} = \frac{( x y + 3 x - y - 3 )}{x y - 2 x + 4 y - 8}

What is (\partial)/(\partial x)((4x+4)(ln(8xy))) ?
The answer to (\partial)/(\partial x)((4x+4)(ln(8xy))) is 4ln(8xy)+(4x+4)/x