What is the derivative of x^5ln(2x) ?

The derivative of x^5ln(2x) is 5x^4ln(2x)+x^4

What is the first derivative of x^5ln(2x) ?

The first derivative of x^5ln(2x) is 5x^4ln(2x)+x^4

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\frac{d}{d x} (x^{5} ln (2 x))

5 x^{4} ln (2 x) + x^{4}

Solution steps

\frac{d}{d x} (x^{5} ln (2 x))

Apply the Product Rule:

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

f = x^{5}, g = ln (2 x)

= \frac{d}{d x} (x^{5}) ln (2 x) + \frac{d}{d x} (ln (2 x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (ln (2 x)) = \frac{1}{x}

= 5 x^{4} ln (2 x) + \frac{1}{x} x^{5}

\frac{1}{x} x^{5} = x^{4}

= 5 x^{4} ln (2 x) + x^{4}

f (x) = (\frac{x ^{2}}{x - 1})^{2}

\int_{0}^{1} 1 d x

\int e^{- 4}

f (x) = - x^{3} + 4 x^{2} - 1, at x = 1

\frac{d}{d x} (e^{- 3 x + 4})

What is the derivative of x^5ln(2x) ?
The derivative of x^5ln(2x) is 5x^4ln(2x)+x^4
What is the first derivative of x^5ln(2x) ?
The first derivative of x^5ln(2x) is 5x^4ln(2x)+x^4