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Popular >

derivative of x^nln(x)

Solution

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

Solution

n x^{n - 1} ln (x) + x^{n - 1}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{n}) = n x^{n - 1}

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

= n x^{n - 1} ln (x) + \frac{1}{x} x^{n}

\frac{1}{x} x^{n} = x^{n - 1}

= n x^{n - 1} ln (x) + x^{n - 1}

Popular Examples

inverse oflaplace 9/((s+3)^2)inverse laplace

\frac{9}{( s + 3 ) ^{2}}

limit as x approaches 4 of e^4-x

x \to 4 lim (e^{4} - x)

derivative of-4/5 e^{(2/3 x})

\frac{d}{d x} (- \frac{4}{5} e^{(\frac{2}{3} x)})

derivative of (1+x^2sin(x)^4)

\frac{d}{d x} ((1 + x^{2} sin (x))^{4})

integral of (2x+7)/((2x^2+14x)^4)

\int \frac{2 x + 7}{( 2 x ^{2} + 14 x ) ^{4}} d x

Frequently Asked Questions (FAQ)

What is the derivative of x^nln(x) ?
The derivative of x^nln(x) is nx^{n-1}ln(x)+x^{n-1}
What is the first derivative of x^nln(x) ?
The first derivative of x^nln(x) is nx^{n-1}ln(x)+x^{n-1}