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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

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

\frac{d y}{d x} = - \frac{3 x}{y}

\frac{d}{d x} ((x^{2} + 3 x - 11)^{50})

\frac{d}{d x} (e^{a t} sin (b t))

\int 3 x^{- 2} d x

\int cos (4 θ) d θ

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