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Popular >

derivative of x^6ln(5x)

Solution

\frac{d}{d x} (x^{6} ln (5 x))

Solution

6 x^{5} ln (5 x) + x^{5}

Solution steps

\frac{d}{d x} (x^{6} ln (5 x))

Apply the Product Rule:

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

f = x^{6}, g = ln (5 x)

= \frac{d}{d x} (x^{6}) ln (5 x) + \frac{d}{d x} (ln (5 x)) x^{6}

\frac{d}{d x} (x^{6}) = 6 x^{5}

\frac{d}{d x} (ln (5 x)) = \frac{1}{x}

= 6 x^{5} ln (5 x) + \frac{1}{x} x^{6}

\frac{1}{x} x^{6} = x^{5}

= 6 x^{5} ln (5 x) + x^{5}

Graph

Popular Examples

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f (x) = 20 x

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x \to 0 lim (\frac{sin ( 13 x )}{x})

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\int \frac{2900}{1 + 0.25 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of x^6ln(5x) ?
The derivative of x^6ln(5x) is 6x^5ln(5x)+x^5
What is the first derivative of x^6ln(5x) ?
The first derivative of x^6ln(5x) is 6x^5ln(5x)+x^5