What is the derivative of x^9ln(7x) ?

The derivative of x^9ln(7x) is 9x^8ln(7x)+x^8

What is the first derivative of x^9ln(7x) ?

The first derivative of x^9ln(7x) is 9x^8ln(7x)+x^8

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\frac{d}{d x} (x^{9} ln (7 x))

9 x^{8} ln (7 x) + x^{8}

Solution steps

\frac{d}{d x} (x^{9} ln (7 x))

Apply the Product Rule:

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

f = x^{9}, g = ln (7 x)

= \frac{d}{d x} (x^{9}) ln (7 x) + \frac{d}{d x} (ln (7 x)) x^{9}

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

\frac{d}{d x} (ln (7 x)) = \frac{1}{x}

= 9 x^{8} ln (7 x) + \frac{1}{x} x^{9}

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

= 9 x^{8} ln (7 x) + x^{8}

What is the derivative of x^9ln(7x) ?
The derivative of x^9ln(7x) is 9x^8ln(7x)+x^8
What is the first derivative of x^9ln(7x) ?
The first derivative of x^9ln(7x) is 9x^8ln(7x)+x^8