What is the derivative of x^9ln(4x) ?

The derivative of x^9ln(4x) is 9x^8ln(4x)+x^8

What is the first derivative of x^9ln(4x) ?

The first derivative of x^9ln(4x) is 9x^8ln(4x)+x^8

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\frac{d}{d x} (x^{9} ln (4 x))

9 x^{8} ln (4 x) + x^{8}

Solution steps

\frac{d}{d x} (x^{9} ln (4 x))

Apply the Product Rule:

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

f = x^{9}, g = ln (4 x)

= \frac{d}{d x} (x^{9}) ln (4 x) + \frac{d}{d x} (ln (4 x)) x^{9}

\frac{d}{d x} (x^{9}) = 9 x^{8}

\frac{d}{d x} (ln (4 x)) = \frac{1}{x}

= 9 x^{8} ln (4 x) + \frac{1}{x} x^{9}

\frac{1}{x} x^{9} = x^{8}

= 9 x^{8} ln (4 x) + x^{8}

\frac{d}{d t} (3)

f (x) = ln (4)

x d x + (x^{2} y + 4 y) d y = 0, y (4) = 0

What is the derivative of x^9ln(4x) ?
The derivative of x^9ln(4x) is 9x^8ln(4x)+x^8
What is the first derivative of x^9ln(4x) ?
The first derivative of x^9ln(4x) is 9x^8ln(4x)+x^8