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Popular >

derivative of x(ln(x^2))

Solution

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

Solution

2 ln (x) + 2

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

1 \cdot ln (x^{2}) + \frac{2}{x} x : 2 ln (x) + 2

= 2 ln (x) + 2

Popular Examples

integral of sin^6(2x)

\int sin^{6} (2 x) d x

x^{''}+3x^'+4x=0,x(0)=3,x^'(0)=1

x^{^{''}} + 3 x^{^{'}} + 4 x = 0, x (0) = 3, x^{^{'}} (0) = 1

derivative of-(e^{-|x|}x/(|x|))

\frac{d}{d x} (- \frac{e ^{- ∣ x ∣} x}{∣ x ∣})

(\partial)/(\partial x)(2t^2+2x)

\frac{\partial}{\partial x} (2 t^{2} + 2 x)

(\partial)/(\partial x)(2y-3x)

\frac{\partial}{\partial x} (2 y - 3 x)

Frequently Asked Questions (FAQ)

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