What is the derivative of x^8ln(9x) ?

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{8}, g = ln (9 x)

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

\frac{d}{d x} (x^{8}) = 8 x^{7}

\frac{d}{d x} (ln (9 x)) = \frac{1}{x}

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

\frac{1}{x} x^{8} = x^{7}

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

y^{^{'}} + 2 y = 3, y (0) = 0

\frac{d}{d x} (4^{s i n^{2} (x) + c o s (3 x)})

2 ln (x) + 6

\frac{\partial}{\partial x} (x y - x - y + 1)

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