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Popular >

derivative of f(x)=xln(x^2)

Solution

derivative of

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

Solution

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

= ln (x^{2}) + 2

Graph

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slope of (-2,-4),(-3,-3)slope

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(\partial)/(\partial x)(e^{xy}y)

\frac{\partial}{\partial x} (e^{x y} y)

derivative of (x+1/x ^2)

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

(\partial)/(\partial x)(e^xx)

\frac{\partial}{\partial x} (e^{x} x)

(\partial)/(\partial y)(-1/y)

\frac{\partial}{\partial y} (- \frac{1}{y})

Frequently Asked Questions (FAQ)

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