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

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

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}

\frac{d}{d x} (- 2 cos (x) sin (x) - 2 cos (x))

\int \frac{1}{( x - 2 ) ^{4}} d x

x \to π lim (\frac{tan ( x )}{sin ( 2 x )})

\frac{d}{d x} (x + y + z)

\frac{d}{d x} (e^{x} + e^{x})

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