What is the derivative of x^{12}ln(x) ?

The derivative of x^{12}ln(x) is 12x^{11}ln(x)+x^{11}

What is the first derivative of x^{12}ln(x) ?

The first derivative of x^{12}ln(x) is 12x^{11}ln(x)+x^{11}

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\frac{d}{d x} (x^{12} ln (x))

12 x^{11} ln (x) + x^{11}

Solution steps

\frac{d}{d x} (x^{12} ln (x))

Apply the Product Rule:

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

f = x^{12}, g = ln (x)

= \frac{d}{d x} (x^{12}) ln (x) + \frac{d}{d x} (ln (x)) x^{12}

\frac{d}{d x} (x^{12}) = 12 x^{11}

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

= 12 x^{11} ln (x) + \frac{1}{x} x^{12}

\frac{1}{x} x^{12} = x^{11}

= 12 x^{11} ln (x) + x^{11}

What is the derivative of x^{12}ln(x) ?
The derivative of x^{12}ln(x) is 12x^{11}ln(x)+x^{11}
What is the first derivative of x^{12}ln(x) ?
The first derivative of x^{12}ln(x) is 12x^{11}ln(x)+x^{11}