What is the derivative of (x^2ln(sqrt(x))/(1+2x)) ?

The derivative of (x^2ln(sqrt(x))/(1+2x)) is (2x^2ln(x)+2x^2+2xln(x)+x)/(2(1+2x)^2)

What is the first derivative of (x^2ln(sqrt(x))/(1+2x)) ?

The first derivative of (x^2ln(sqrt(x))/(1+2x)) is (2x^2ln(x)+2x^2+2xln(x)+x)/(2(1+2x)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

x - 7

- 10 x^{2} y + \frac{d y}{d x} = - 7 x^{2}

\int 1000 x d x

\int_{0}^{1} \frac{4 x}{( x ^{2} + 1 ) ^{2}} d x

x \to 5 lim (\frac{3 x + 5}{5 x + 6})

What is the derivative of (x^2ln(sqrt(x))/(1+2x)) ?
The derivative of (x^2ln(sqrt(x))/(1+2x)) is (2x^2ln(x)+2x^2+2xln(x)+x)/(2(1+2x)^2)
What is the first derivative of (x^2ln(sqrt(x))/(1+2x)) ?
The first derivative of (x^2ln(sqrt(x))/(1+2x)) is (2x^2ln(x)+2x^2+2xln(x)+x)/(2(1+2x)^2)