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Popular >

derivative of 3x^8ln(x)

Solution

\frac{d}{d x} (3 x^{8} ln (x))

Solution

3 (8 x^{7} ln (x) + x^{7})

Solution steps

\frac{d}{d x} (3 x^{8} ln (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (x^{8} ln (x))

Apply the Product Rule:

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

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

= 3 (\frac{d}{d x} (x^{8}) ln (x) + \frac{d}{d x} (ln (x)) x^{8})

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

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

= 3 (8 x^{7} ln (x) + \frac{1}{x} x^{8})

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

= 3 (8 x^{7} ln (x) + x^{7})

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 3x^8ln(x) ?
The derivative of 3x^8ln(x) is 3(8x^7ln(x)+x^7)
What is the first derivative of 3x^8ln(x) ?
The first derivative of 3x^8ln(x) is 3(8x^7ln(x)+x^7)