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

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

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

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

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derivative of

f (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 x} (1. 8^{0.045 x} - 1)

\int \frac{y ^{2} + 2 y + 1}{y} d y

\frac{4 x}{x + 3} (1.1)

n = 0 \sum \infty e^{- 4 n}

y = \frac{x ^{6}}{2 - x ^{5}}

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