What is the derivative of x^5ln(8x) ?

The derivative of x^5ln(8x) is 5x^4ln(8x)+x^4

What is the first derivative of x^5ln(8x) ?

The first derivative of x^5ln(8x) is 5x^4ln(8x)+x^4

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\frac{d}{d x} (x^{5} ln (8 x))

5 x^{4} ln (8 x) + x^{4}

Solution steps

\frac{d}{d x} (x^{5} ln (8 x))

Apply the Product Rule:

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

f = x^{5}, g = ln (8 x)

= \frac{d}{d x} (x^{5}) ln (8 x) + \frac{d}{d x} (ln (8 x)) x^{5}

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

\frac{d}{d x} (ln (8 x)) = \frac{1}{x}

= 5 x^{4} ln (8 x) + \frac{1}{x} x^{5}

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

= 5 x^{4} ln (8 x) + x^{4}

\int \frac{5 x ^{2}}{( 49 + x ^{2} ) ^{2}} d x

y = \frac{2 x}{x - 1}, (- 1, 1)

\frac{d}{d x} (x^{a x})

\frac{d}{d x} (x x^{2} + 4)

\int (2 x + 2) d x

What is the derivative of x^5ln(8x) ?
The derivative of x^5ln(8x) is 5x^4ln(8x)+x^4
What is the first derivative of x^5ln(8x) ?
The first derivative of x^5ln(8x) is 5x^4ln(8x)+x^4