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Popular >

derivative of 3x^2ln(x)

Solution

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

Solution

3 (2 x ln (x) + x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x^{2}, g = ln (x)

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

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

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

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

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

= 3 (2 x ln (x) + x)

Popular Examples

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derivative of e^x(sin(x-cos(x)))

\frac{d}{d x} (e^{x} (sin (x) - cos (x)))

area x^2,12-x,-4,3 area

x^{2}, 12 - x, - 4, 3

integral of (-x^4+1)^2(-4x^3)

\int (- x^{4} + 1)^{2} (- 4 x^{3}) d x

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\int \frac{1}{x ^{2} - 2} d x

Frequently Asked Questions (FAQ)

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