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Popular >

derivative of (xln(x)^2)

Solution

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

Solution

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

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

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

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

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

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

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

Popular Examples

(\partial)/(\partial x)(sqrt(x^2+2xy+y^4))

\frac{\partial}{\partial x} (x^{2} + 2 x y + y^{4})

tangent of f(x)= 4/x ,(-9,-4/9)tangent of

f (x) = \frac{4}{x}, (- 9, - \frac{4}{9})

(\partial)/(\partial y)(x+y-8)

\frac{\partial}{\partial y} (x + y - 8)

integral from 0 to 8 of 1/(\sqrt[3]{x)}

(\partial)/(\partial x)(e^{x^2}+2y^3)

\frac{\partial}{\partial x} (e^{x^{2}} + 2 y^{3})

Frequently Asked Questions (FAQ)

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