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Popular Calculus >

derivative of x^6ln(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

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

Graph

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Frequently Asked Questions (FAQ)

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