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Popular >

derivative of x^3*ln(x)

Solution

\frac{d}{d x} (x^{3} \cdot ln (x))

Solution

3 x^{2} ln (x) + x^{2}

Solution steps

\frac{d}{d x} (x^{3} ln (x))

Apply the Product Rule:

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

f = x^{3}, g = ln (x)

= \frac{d}{d x} (x^{3}) ln (x) + \frac{d}{d x} (ln (x)) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 3 x^{2} ln (x) + \frac{1}{x} x^{3}

\frac{1}{x} x^{3} = x^{2}

= 3 x^{2} ln (x) + x^{2}

Popular Examples

derivative of y=y derivative of

y = y

roots (kx)/(a^2+x^2)roots

\frac{k x}{a ^{2} + x ^{2}}

tangent of f(x)=sqrt(x)(x-2),\at x=1 tangent of

f (x) = x (x - 2), at x = 1

integral from 0 to 2 of x^3e^x

\int_{0}^{2} x^{3} e^{x} d x

limit as x approaches 4-of (x-9)/(x-4)

x \to 4 - lim (\frac{x - 9}{x - 4})

Frequently Asked Questions (FAQ)

What is the derivative of x^3*ln(x) ?
The derivative of x^3*ln(x) is 3x^2ln(x)+x^2
What is the first derivative of x^3*ln(x) ?
The first derivative of x^3*ln(x) is 3x^2ln(x)+x^2